{"id":4029,"date":"2020-10-24T16:19:16","date_gmt":"2020-10-24T16:19:16","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-financialaccounting\/?post_type=chapter&#038;p=4029"},"modified":"2020-11-17T18:48:33","modified_gmt":"2020-11-17T18:48:33","slug":"effective-interest-rate","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-clinton-financialaccounting\/chapter\/effective-interest-rate\/","title":{"raw":"Effective Interest Rate","rendered":"Effective Interest Rate"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\">Discuss the effective interest rate method of amortizing bond premium and discount<\/li>\r\n<\/ul>\r\n<\/div>\r\nRather than using the straight line method of amortizing discounts or premiums, the preferable approach to recording amortization is the effective-interest method that uses a constant percentage of the carrying value, rather than an equal dollar amount each year, similar to the double-declining balance method of depreciation or fixed assets.\r\n\r\nThe amount of amortization is the difference between the cash paid for interest and the calculated amount of bond interest expense, and at the end of the bond carrying period, the unamortized discount or premium would be zero.\r\n\r\nLet\u2019s take a look at the concept of effective interest rate from the bond investor\u2019s point of view.\r\n\r\n<img class=\"alignright wp-image-4967 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5107\/2020\/10\/02222515\/tesla-1738969_1920-300x200.jpg\" alt=\"A black Tesla car hooked up to a Tesla charging station.\" width=\"300\" height=\"200\" \/>\r\n\r\nFor instance, on March 5, 2014, Tesla Inc. (TSLA) issued $1.2 billion in fixed-rate bonds ($1,000 face value each, so 1.2 million bonds) with a maturity date of March 01, 2021, and a fixed coupon rate of 1.25%, payable semi-annually. The debt received an S&amp;P rating of B- when it was issued. So each bond of $1,000 pays $12.50 per year, but the average investor may be looking for something like 7%, or 10%, depending on what else is available in the market, so let\u2019s say the investor paid $625 for one of the $1000 bonds. The $12.50 per year in interest on a $625 investment is still only a 2% return, but when (if) the bond matures 7 years later, the investor also gains an additional $375 over what was paid for the bond. In this case, the effective rate would be a 7% ROI on the difference between the investment and the maturity value, plus the 2% coupon rate, for a combined yield of 9%.\r\n\r\nTo find the ROI on the investment, divide the maturity value by the purchase price (1000\/625 = 1.6). Find a future value table of $1. On that table, find the row for n=7 (7 years). Look for a factor close to 1.6 (you should find it in the column for 7% annual return.)\u00a0 You could check this mathematically by taking 625 * 1.077 which would give you the future value of 625 invested for 7 years at 7% compounded annually (it comes to $1,003.61 which is close enough for this purpose).\r\n\r\nAssume that Premium Corp. issues 100, five-year, semi-annual, $1,000 bonds with an 8% coupon. Premium Corp. receives $108,530 because the market rate is 6% (the bonds sold at a premium because the coupon rate was higher than the market rate).\r\n\r\nInstead of just dividing the premium by five to get the annual amortization (or by 10 to get the semi-annual adjustment), Premium Corp. uses the effective interest method to amortize the premium. For the first payment, we multiply the carrying amount of $108,530 by 6% and then divide that by two (or multiply by half) = $3,255.90.\r\n\r\nThe coupon payment is $4,000 (cash disbursement) but the interest expense is only $3,255.90. Therefore the premium amortization is $744.10 ($4,000 \u2013 $3,255.90). The premium amortization reduces the net book value of the debt to $107,785.90 ($108,530 \u2013 $744.10). This new balance would then be used to calculate the effective interest for the next period. This process would be repeated each period, as shown in the following table:\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th scope=\"col\">Period ending<\/th>\r\n<th scope=\"col\">Book Value<\/th>\r\n<th scope=\"col\">Interest expense at 6%, semi-annual<\/th>\r\n<th scope=\"col\">Coupon Payment<\/th>\r\n<th scope=\"col\">Premium Amortization<\/th>\r\n<th scope=\"col\">Book Value, end of period<\/th>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X1<\/td>\r\n<td class=\"r\">108,530.00<\/td>\r\n<td class=\"r\">3,255.90<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(744.10)<\/td>\r\n<td class=\"r\">107,785.90<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X1<\/td>\r\n<td class=\"r\">107,785.90<\/td>\r\n<td class=\"r\">3,233.58<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(766.42)<\/td>\r\n<td class=\"r\">107,019.48<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X2<\/td>\r\n<td class=\"r\">107,019.48<\/td>\r\n<td class=\"r\">3,210.58<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(789.42)<\/td>\r\n<td class=\"r\">106,230.06<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X2<\/td>\r\n<td class=\"r\">106,230.06<\/td>\r\n<td class=\"r\">3,186.90<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(813.10)<\/td>\r\n<td class=\"r\">105,416.96<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X3<\/td>\r\n<td class=\"r\">105,416.96<\/td>\r\n<td class=\"r\">3,162.51<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(837.49)<\/td>\r\n<td class=\"r\">104,579.47<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X3<\/td>\r\n<td class=\"r\">104,579.47<\/td>\r\n<td class=\"r\">3,137.38<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(862.62)<\/td>\r\n<td class=\"r\">103,716.86<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X4<\/td>\r\n<td class=\"r\">103,716.86<\/td>\r\n<td class=\"r\">3,111.51<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(888.49)<\/td>\r\n<td class=\"r\">102,828.36<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X4<\/td>\r\n<td class=\"r\">102,828.36<\/td>\r\n<td class=\"r\">3,084.85<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(915.15)<\/td>\r\n<td class=\"r\">101,913.21<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X5<\/td>\r\n<td class=\"r\">101,913.21<\/td>\r\n<td class=\"r\">3,057.40<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(942.60)<\/td>\r\n<td class=\"r\">100,970.61<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X5<\/td>\r\n<td class=\"r\">100,970.61<\/td>\r\n<td class=\"r\">3,029.12<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">(970.61)<\/td>\r\n<td class=\"r\">100,000.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nNote that the last amortization amount was adjusted slightly to fully amortize the premium.\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th scope=\"col\">Period ending<\/th>\r\n<th scope=\"col\">Premium<\/th>\r\n<th scope=\"col\">Premium Amortization<\/th>\r\n<th scope=\"col\">Unamortized Premium<\/th>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X1<\/td>\r\n<td class=\"r\">8,530.00<\/td>\r\n<td class=\"r\">(744.10)<\/td>\r\n<td class=\"r\">7,785.90<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">&gt;12\/31\/X1<\/td>\r\n<td class=\"r\">7,785.90<\/td>\r\n<td class=\"r\">(766.42)<\/td>\r\n<td class=\"r\">7,019.48<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X2<\/td>\r\n<td class=\"r\">7,019.48<\/td>\r\n<td class=\"r\">(789.42)<\/td>\r\n<td class=\"r\">6,230.06<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X2<\/td>\r\n<td class=\"r\">6,230.06<\/td>\r\n<td class=\"r\">(813.10)<\/td>\r\n<td class=\"r\">5,416.96<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X3<\/td>\r\n<td class=\"r\">5,416.96<\/td>\r\n<td class=\"r\">(837.49)<\/td>\r\n<td class=\"r\">4,579.47<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X3<\/td>\r\n<td class=\"r\">4,579.47<\/td>\r\n<td class=\"r\">(862.62)<\/td>\r\n<td class=\"r\">3,716.86<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>6\/30\/X4<\/td>\r\n<td class=\"r\">3,716.86<\/td>\r\n<td class=\"r\">(888.49)<\/td>\r\n<td class=\"r\">2,828.36<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X4<\/td>\r\n<td class=\"r\">2,828.36<\/td>\r\n<td class=\"r\">(915.15)<\/td>\r\n<td class=\"r\">1,913.21<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X5<\/td>\r\n<td class=\"r\">1,913.21<\/td>\r\n<td class=\"r\">(942.60)<\/td>\r\n<td class=\"r\">970.61<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X5<\/td>\r\n<td class=\"r\">970.61<\/td>\r\n<td class=\"r\">(970.61)<\/td>\r\n<td class=\"r\">(0.00)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nThe initial journal entry to record the issuance of the bonds and the final journal entry to record repayment at maturity would be identical to those demonstrated for the straight line method. However, each journal entry to record the periodic interest expense recognition would vary and can be determined by reference to the preceding amortization table.\r\n\r\nFor instance, the following entry would record interest on June 30, 20X3:\r\n<table class=\"fin-table gridded\"><caption class=\"u-clearfix\"><span style=\"text-transform: uppercase;\">Journal<\/span><span style=\"float: right;\">Page 101<\/span><\/caption>\r\n<thead>\r\n<tr aria-hidden=\"true\">\r\n<td colspan=\"5\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th scope=\"col\">Date<\/th>\r\n<th scope=\"col\">Description<\/th>\r\n<th scope=\"col\">Post. Ref.<\/th>\r\n<th scope=\"col\">Debit<\/th>\r\n<th scope=\"col\">Credit<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>20X3<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<th scope=\"row\">June 30<\/th>\r\n<td>Interest expense<\/td>\r\n<td class=\"r\"><\/td>\r\n<td class=\"r\">3,162.51<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\r\n<td>Premium on bonds payable<\/td>\r\n<td><\/td>\r\n<td class=\"r\">837.49<\/td>\r\n<td class=\"r\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\r\n<td>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Checking Account<\/td>\r\n<td><\/td>\r\n<td class=\"r\"><\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\r\n<td>To record coupon payment on bonds<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAssume that Discount Corp. issues 100, five-year, semi-annual, $1,000 bonds with an 8% coupon during a period of time when the market rate is 10% and so receives $92,278 because the coupon rate is lower than the market rate.\r\n<div align=\"left\">\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th scope=\"col\">Period ending<\/th>\r\n<th scope=\"col\">Book Value<\/th>\r\n<th scope=\"col\">Interest expense at 10%, semi-annual<\/th>\r\n<th scope=\"col\">Coupon Payment<\/th>\r\n<th scope=\"col\">Discount Amortization<\/th>\r\n<th scope=\"col\">Book Value, end of period<\/th>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X1<\/td>\r\n<td class=\"r\">92,278.00<\/td>\r\n<td class=\"r\">4,613.90<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">613.90<\/td>\r\n<td class=\"r\">92,891.90<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X1<\/td>\r\n<td class=\"r\">92,891.90<\/td>\r\n<td class=\"r\">4,644.60<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">644.60<\/td>\r\n<td class=\"r\">93,536.50<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X2<\/td>\r\n<td class=\"r\">93,536.50<\/td>\r\n<td class=\"r\">4,676.82<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">676.82<\/td>\r\n<td class=\"r\">94,213.32<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X2<\/td>\r\n<td class=\"r\">94,213.32<\/td>\r\n<td class=\"r\">4,710.67<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">710.67<\/td>\r\n<td class=\"r\">94,923.99<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X3<\/td>\r\n<td class=\"r\">94,923.99<\/td>\r\n<td class=\"r\">4,746.20<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">746.20<\/td>\r\n<td class=\"r\">95,670.19<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X3<\/td>\r\n<td class=\"r\">95,670.19<\/td>\r\n<td class=\"r\">4,783.51<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">783.51<\/td>\r\n<td class=\"r\">96,453.69<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X4<\/td>\r\n<td class=\"r\">96,453.69<\/td>\r\n<td class=\"r\">4,822.68<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">822.68<\/td>\r\n<td class=\"r\">97,276.38<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X4<\/td>\r\n<td class=\"r\">97,276.38<\/td>\r\n<td class=\"r\">4,863.82<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">863.82<\/td>\r\n<td class=\"r\">98,140.20<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X5<\/td>\r\n<td class=\"r\">98,140.20<\/td>\r\n<td class=\"r\">4,907.01<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">907.01<\/td>\r\n<td class=\"r\">99,047.21<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X5<\/td>\r\n<td class=\"r\">99,047.21<\/td>\r\n<td class=\"r\">4,952.36<\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<td class=\"r\">952.79<\/td>\r\n<td class=\"r\">100,000.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<th scope=\"col\">Period ending<\/th>\r\n<th scope=\"col\">Discount<\/th>\r\n<th scope=\"col\">Discount Amortization<\/th>\r\n<th scope=\"col\">Unamortized Discount<\/th>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X1<\/td>\r\n<td class=\"r\">7,722.00<\/td>\r\n<td class=\"r\">613.90<\/td>\r\n<td class=\"r\">7,108.10<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X1<\/td>\r\n<td class=\"r\">7,108.10<\/td>\r\n<td class=\"r\">644.60<\/td>\r\n<td class=\"r\">6,463.51<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X2<\/td>\r\n<td class=\"r\">6,463.51<\/td>\r\n<td class=\"r\">676.82<\/td>\r\n<td class=\"r\">5,786.68<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X2<\/td>\r\n<td class=\"r\">5,786.68<\/td>\r\n<td class=\"r\">710.67<\/td>\r\n<td class=\"r\">5,076.01<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X3<\/td>\r\n<td class=\"r\">5,076.01<\/td>\r\n<td class=\"r\">746.20<\/td>\r\n<td class=\"r\">4,329.81<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X3<\/td>\r\n<td class=\"r\">4,329.81<\/td>\r\n<td class=\"r\">783.51<\/td>\r\n<td class=\"r\">3,546.31<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X4<\/td>\r\n<td class=\"r\">3,546.31<\/td>\r\n<td class=\"r\">822.68<\/td>\r\n<td class=\"r\">2,723.62<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X4<\/td>\r\n<td class=\"r\">2,723.62<\/td>\r\n<td class=\"r\">863.82<\/td>\r\n<td class=\"r\">1,859.80<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">6\/30\/X5<\/td>\r\n<td class=\"r\">1,859.80<\/td>\r\n<td class=\"r\">907.01<\/td>\r\n<td class=\"r\">952.79<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">12\/31\/X5<\/td>\r\n<td class=\"r\">952.79<\/td>\r\n<td class=\"r\">952.79<\/td>\r\n<td class=\"r\">0.00<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nEach journal entry to record the periodic interest expense recognition would vary, and can be determined by reference to the preceding amortization table. For instance, the following entry would record interest on June 30, 20X3:\r\n<table class=\"fin-table gridded\"><caption class=\"u-clearfix\"><span style=\"text-transform: uppercase;\">Journal<\/span><span style=\"float: right;\">Page 101<\/span><\/caption>\r\n<thead>\r\n<tr aria-hidden=\"true\">\r\n<td colspan=\"5\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<th scope=\"col\">Date<\/th>\r\n<th scope=\"col\">Description<\/th>\r\n<th scope=\"col\">Post. Ref.<\/th>\r\n<th scope=\"col\">Debit<\/th>\r\n<th scope=\"col\">Credit<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>20X3<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<th scope=\"row\">June 30<\/th>\r\n<td>Interest expense<\/td>\r\n<td class=\"r\"><\/td>\r\n<td class=\"r\">4,746.20<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\r\n<td>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Discount on bonds payable<\/td>\r\n<td><\/td>\r\n<td class=\"r\"><\/td>\r\n<td class=\"r\">746.20<\/td>\r\n<\/tr>\r\n<tr>\r\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\r\n<td>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Checking Account<\/td>\r\n<td><\/td>\r\n<td class=\"r\"><\/td>\r\n<td class=\"r\">4,000.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\r\n<td>To record coupon payment on bonds<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNow that you understand the effective interest rate method of amortizing bond premiums and discounts we\u2019ll move on to other long-term liabilities.\r\n<div class=\"textbox tryit\">\r\n<h3>PRACTICE QUESTION<\/h3>\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/23818\r\n\r\nhttps:\/\/assessments.lumenlearning.com\/assessments\/23819\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li style=\"font-weight: 400;\">Discuss the effective interest rate method of amortizing bond premium and discount<\/li>\n<\/ul>\n<\/div>\n<p>Rather than using the straight line method of amortizing discounts or premiums, the preferable approach to recording amortization is the effective-interest method that uses a constant percentage of the carrying value, rather than an equal dollar amount each year, similar to the double-declining balance method of depreciation or fixed assets.<\/p>\n<p>The amount of amortization is the difference between the cash paid for interest and the calculated amount of bond interest expense, and at the end of the bond carrying period, the unamortized discount or premium would be zero.<\/p>\n<p>Let\u2019s take a look at the concept of effective interest rate from the bond investor\u2019s point of view.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-4967 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5107\/2020\/10\/02222515\/tesla-1738969_1920-300x200.jpg\" alt=\"A black Tesla car hooked up to a Tesla charging station.\" width=\"300\" height=\"200\" \/><\/p>\n<p>For instance, on March 5, 2014, Tesla Inc. (TSLA) issued $1.2 billion in fixed-rate bonds ($1,000 face value each, so 1.2 million bonds) with a maturity date of March 01, 2021, and a fixed coupon rate of 1.25%, payable semi-annually. The debt received an S&amp;P rating of B- when it was issued. So each bond of $1,000 pays $12.50 per year, but the average investor may be looking for something like 7%, or 10%, depending on what else is available in the market, so let\u2019s say the investor paid $625 for one of the $1000 bonds. The $12.50 per year in interest on a $625 investment is still only a 2% return, but when (if) the bond matures 7 years later, the investor also gains an additional $375 over what was paid for the bond. In this case, the effective rate would be a 7% ROI on the difference between the investment and the maturity value, plus the 2% coupon rate, for a combined yield of 9%.<\/p>\n<p>To find the ROI on the investment, divide the maturity value by the purchase price (1000\/625 = 1.6). Find a future value table of $1. On that table, find the row for n=7 (7 years). Look for a factor close to 1.6 (you should find it in the column for 7% annual return.)\u00a0 You could check this mathematically by taking 625 * 1.077 which would give you the future value of 625 invested for 7 years at 7% compounded annually (it comes to $1,003.61 which is close enough for this purpose).<\/p>\n<p>Assume that Premium Corp. issues 100, five-year, semi-annual, $1,000 bonds with an 8% coupon. Premium Corp. receives $108,530 because the market rate is 6% (the bonds sold at a premium because the coupon rate was higher than the market rate).<\/p>\n<p>Instead of just dividing the premium by five to get the annual amortization (or by 10 to get the semi-annual adjustment), Premium Corp. uses the effective interest method to amortize the premium. For the first payment, we multiply the carrying amount of $108,530 by 6% and then divide that by two (or multiply by half) = $3,255.90.<\/p>\n<p>The coupon payment is $4,000 (cash disbursement) but the interest expense is only $3,255.90. Therefore the premium amortization is $744.10 ($4,000 \u2013 $3,255.90). The premium amortization reduces the net book value of the debt to $107,785.90 ($108,530 \u2013 $744.10). This new balance would then be used to calculate the effective interest for the next period. This process would be repeated each period, as shown in the following table:<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<th scope=\"col\">Period ending<\/th>\n<th scope=\"col\">Book Value<\/th>\n<th scope=\"col\">Interest expense at 6%, semi-annual<\/th>\n<th scope=\"col\">Coupon Payment<\/th>\n<th scope=\"col\">Premium Amortization<\/th>\n<th scope=\"col\">Book Value, end of period<\/th>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X1<\/td>\n<td class=\"r\">108,530.00<\/td>\n<td class=\"r\">3,255.90<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(744.10)<\/td>\n<td class=\"r\">107,785.90<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X1<\/td>\n<td class=\"r\">107,785.90<\/td>\n<td class=\"r\">3,233.58<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(766.42)<\/td>\n<td class=\"r\">107,019.48<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X2<\/td>\n<td class=\"r\">107,019.48<\/td>\n<td class=\"r\">3,210.58<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(789.42)<\/td>\n<td class=\"r\">106,230.06<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X2<\/td>\n<td class=\"r\">106,230.06<\/td>\n<td class=\"r\">3,186.90<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(813.10)<\/td>\n<td class=\"r\">105,416.96<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X3<\/td>\n<td class=\"r\">105,416.96<\/td>\n<td class=\"r\">3,162.51<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(837.49)<\/td>\n<td class=\"r\">104,579.47<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X3<\/td>\n<td class=\"r\">104,579.47<\/td>\n<td class=\"r\">3,137.38<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(862.62)<\/td>\n<td class=\"r\">103,716.86<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X4<\/td>\n<td class=\"r\">103,716.86<\/td>\n<td class=\"r\">3,111.51<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(888.49)<\/td>\n<td class=\"r\">102,828.36<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X4<\/td>\n<td class=\"r\">102,828.36<\/td>\n<td class=\"r\">3,084.85<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(915.15)<\/td>\n<td class=\"r\">101,913.21<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X5<\/td>\n<td class=\"r\">101,913.21<\/td>\n<td class=\"r\">3,057.40<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(942.60)<\/td>\n<td class=\"r\">100,970.61<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X5<\/td>\n<td class=\"r\">100,970.61<\/td>\n<td class=\"r\">3,029.12<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">(970.61)<\/td>\n<td class=\"r\">100,000.00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Note that the last amortization amount was adjusted slightly to fully amortize the premium.<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<th scope=\"col\">Period ending<\/th>\n<th scope=\"col\">Premium<\/th>\n<th scope=\"col\">Premium Amortization<\/th>\n<th scope=\"col\">Unamortized Premium<\/th>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X1<\/td>\n<td class=\"r\">8,530.00<\/td>\n<td class=\"r\">(744.10)<\/td>\n<td class=\"r\">7,785.90<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">&gt;12\/31\/X1<\/td>\n<td class=\"r\">7,785.90<\/td>\n<td class=\"r\">(766.42)<\/td>\n<td class=\"r\">7,019.48<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X2<\/td>\n<td class=\"r\">7,019.48<\/td>\n<td class=\"r\">(789.42)<\/td>\n<td class=\"r\">6,230.06<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X2<\/td>\n<td class=\"r\">6,230.06<\/td>\n<td class=\"r\">(813.10)<\/td>\n<td class=\"r\">5,416.96<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X3<\/td>\n<td class=\"r\">5,416.96<\/td>\n<td class=\"r\">(837.49)<\/td>\n<td class=\"r\">4,579.47<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X3<\/td>\n<td class=\"r\">4,579.47<\/td>\n<td class=\"r\">(862.62)<\/td>\n<td class=\"r\">3,716.86<\/td>\n<\/tr>\n<tr>\n<td>6\/30\/X4<\/td>\n<td class=\"r\">3,716.86<\/td>\n<td class=\"r\">(888.49)<\/td>\n<td class=\"r\">2,828.36<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X4<\/td>\n<td class=\"r\">2,828.36<\/td>\n<td class=\"r\">(915.15)<\/td>\n<td class=\"r\">1,913.21<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X5<\/td>\n<td class=\"r\">1,913.21<\/td>\n<td class=\"r\">(942.60)<\/td>\n<td class=\"r\">970.61<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X5<\/td>\n<td class=\"r\">970.61<\/td>\n<td class=\"r\">(970.61)<\/td>\n<td class=\"r\">(0.00)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>The initial journal entry to record the issuance of the bonds and the final journal entry to record repayment at maturity would be identical to those demonstrated for the straight line method. However, each journal entry to record the periodic interest expense recognition would vary and can be determined by reference to the preceding amortization table.<\/p>\n<p>For instance, the following entry would record interest on June 30, 20X3:<\/p>\n<table class=\"fin-table gridded\">\n<caption class=\"u-clearfix\"><span style=\"text-transform: uppercase;\">Journal<\/span><span style=\"float: right;\">Page 101<\/span><\/caption>\n<thead>\n<tr aria-hidden=\"true\">\n<td colspan=\"5\"><\/td>\n<\/tr>\n<tr>\n<th scope=\"col\">Date<\/th>\n<th scope=\"col\">Description<\/th>\n<th scope=\"col\">Post. Ref.<\/th>\n<th scope=\"col\">Debit<\/th>\n<th scope=\"col\">Credit<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>20X3<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<th scope=\"row\">June 30<\/th>\n<td>Interest expense<\/td>\n<td class=\"r\"><\/td>\n<td class=\"r\">3,162.51<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\n<td>Premium on bonds payable<\/td>\n<td><\/td>\n<td class=\"r\">837.49<\/td>\n<td class=\"r\"><\/td>\n<\/tr>\n<tr>\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\n<td>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Checking Account<\/td>\n<td><\/td>\n<td class=\"r\"><\/td>\n<td class=\"r\">4,000.00<\/td>\n<\/tr>\n<tr>\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\n<td>To record coupon payment on bonds<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Assume that Discount Corp. issues 100, five-year, semi-annual, $1,000 bonds with an 8% coupon during a period of time when the market rate is 10% and so receives $92,278 because the coupon rate is lower than the market rate.<\/p>\n<div style=\"text-align: left;\">\n<table>\n<tbody>\n<tr>\n<th scope=\"col\">Period ending<\/th>\n<th scope=\"col\">Book Value<\/th>\n<th scope=\"col\">Interest expense at 10%, semi-annual<\/th>\n<th scope=\"col\">Coupon Payment<\/th>\n<th scope=\"col\">Discount Amortization<\/th>\n<th scope=\"col\">Book Value, end of period<\/th>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X1<\/td>\n<td class=\"r\">92,278.00<\/td>\n<td class=\"r\">4,613.90<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">613.90<\/td>\n<td class=\"r\">92,891.90<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X1<\/td>\n<td class=\"r\">92,891.90<\/td>\n<td class=\"r\">4,644.60<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">644.60<\/td>\n<td class=\"r\">93,536.50<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X2<\/td>\n<td class=\"r\">93,536.50<\/td>\n<td class=\"r\">4,676.82<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">676.82<\/td>\n<td class=\"r\">94,213.32<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X2<\/td>\n<td class=\"r\">94,213.32<\/td>\n<td class=\"r\">4,710.67<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">710.67<\/td>\n<td class=\"r\">94,923.99<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X3<\/td>\n<td class=\"r\">94,923.99<\/td>\n<td class=\"r\">4,746.20<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">746.20<\/td>\n<td class=\"r\">95,670.19<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X3<\/td>\n<td class=\"r\">95,670.19<\/td>\n<td class=\"r\">4,783.51<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">783.51<\/td>\n<td class=\"r\">96,453.69<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X4<\/td>\n<td class=\"r\">96,453.69<\/td>\n<td class=\"r\">4,822.68<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">822.68<\/td>\n<td class=\"r\">97,276.38<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X4<\/td>\n<td class=\"r\">97,276.38<\/td>\n<td class=\"r\">4,863.82<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">863.82<\/td>\n<td class=\"r\">98,140.20<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X5<\/td>\n<td class=\"r\">98,140.20<\/td>\n<td class=\"r\">4,907.01<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">907.01<\/td>\n<td class=\"r\">99,047.21<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X5<\/td>\n<td class=\"r\">99,047.21<\/td>\n<td class=\"r\">4,952.36<\/td>\n<td class=\"r\">4,000.00<\/td>\n<td class=\"r\">952.79<\/td>\n<td class=\"r\">100,000.00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table>\n<tbody>\n<tr>\n<th scope=\"col\">Period ending<\/th>\n<th scope=\"col\">Discount<\/th>\n<th scope=\"col\">Discount Amortization<\/th>\n<th scope=\"col\">Unamortized Discount<\/th>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X1<\/td>\n<td class=\"r\">7,722.00<\/td>\n<td class=\"r\">613.90<\/td>\n<td class=\"r\">7,108.10<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X1<\/td>\n<td class=\"r\">7,108.10<\/td>\n<td class=\"r\">644.60<\/td>\n<td class=\"r\">6,463.51<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X2<\/td>\n<td class=\"r\">6,463.51<\/td>\n<td class=\"r\">676.82<\/td>\n<td class=\"r\">5,786.68<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X2<\/td>\n<td class=\"r\">5,786.68<\/td>\n<td class=\"r\">710.67<\/td>\n<td class=\"r\">5,076.01<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X3<\/td>\n<td class=\"r\">5,076.01<\/td>\n<td class=\"r\">746.20<\/td>\n<td class=\"r\">4,329.81<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X3<\/td>\n<td class=\"r\">4,329.81<\/td>\n<td class=\"r\">783.51<\/td>\n<td class=\"r\">3,546.31<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X4<\/td>\n<td class=\"r\">3,546.31<\/td>\n<td class=\"r\">822.68<\/td>\n<td class=\"r\">2,723.62<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X4<\/td>\n<td class=\"r\">2,723.62<\/td>\n<td class=\"r\">863.82<\/td>\n<td class=\"r\">1,859.80<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">6\/30\/X5<\/td>\n<td class=\"r\">1,859.80<\/td>\n<td class=\"r\">907.01<\/td>\n<td class=\"r\">952.79<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">12\/31\/X5<\/td>\n<td class=\"r\">952.79<\/td>\n<td class=\"r\">952.79<\/td>\n<td class=\"r\">0.00<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Each journal entry to record the periodic interest expense recognition would vary, and can be determined by reference to the preceding amortization table. For instance, the following entry would record interest on June 30, 20X3:<\/p>\n<table class=\"fin-table gridded\">\n<caption class=\"u-clearfix\"><span style=\"text-transform: uppercase;\">Journal<\/span><span style=\"float: right;\">Page 101<\/span><\/caption>\n<thead>\n<tr aria-hidden=\"true\">\n<td colspan=\"5\"><\/td>\n<\/tr>\n<tr>\n<th scope=\"col\">Date<\/th>\n<th scope=\"col\">Description<\/th>\n<th scope=\"col\">Post. Ref.<\/th>\n<th scope=\"col\">Debit<\/th>\n<th scope=\"col\">Credit<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>20X3<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<th scope=\"row\">June 30<\/th>\n<td>Interest expense<\/td>\n<td class=\"r\"><\/td>\n<td class=\"r\">4,746.20<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\n<td>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Discount on bonds payable<\/td>\n<td><\/td>\n<td class=\"r\"><\/td>\n<td class=\"r\">746.20<\/td>\n<\/tr>\n<tr>\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\n<td>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Checking Account<\/td>\n<td><\/td>\n<td class=\"r\"><\/td>\n<td class=\"r\">4,000.00<\/td>\n<\/tr>\n<tr>\n<th><span class=\"u-sr-only\">June 30<\/span><\/th>\n<td>To record coupon payment on bonds<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Now that you understand the effective interest rate method of amortizing bond premiums and discounts we\u2019ll move on to other long-term liabilities.<\/p>\n<div class=\"textbox tryit\">\n<h3>PRACTICE QUESTION<\/h3>\n<p>\t<iframe id=\"lumen_assessment_23818\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=23818&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_23818\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<p>\t<iframe id=\"lumen_assessment_23819\" class=\"resizable\" src=\"https:\/\/assessments.lumenlearning.com\/assessments\/load?assessment_id=23819&#38;embed=1&#38;external_user_id=&#38;external_context_id=&#38;iframe_resize_id=lumen_assessment_23819\" frameborder=\"0\" style=\"border:none;width:100%;height:100%;min-height:400px;\"><br \/>\n\t<\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4029\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Effective Interest Rate. <strong>Authored by<\/strong>: Joseph Cooke. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li><strong>Authored by<\/strong>: Blomst. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/photos\/tesla-tesla-model-x-charging-1738969\/\">https:\/\/pixabay.com\/photos\/tesla-tesla-model-x-charging-1738969\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em>. <strong>License Terms<\/strong>: https:\/\/pixabay.com\/service\/terms\/#license<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":90270,"menu_order":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Effective Interest Rate\",\"author\":\"Joseph Cooke\",\"organization\":\"Lumen 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