Home / Questions / In many financialtransactions, interest is computed and charged more than once ayear. Inte
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In many financialtransactions, interest is computed and charged more than once ayear. Interest on corporate bonds, for example, is usually payableevery six months. |
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Consider a loantransaction in which interest is charged at the rate of 1 percentper month. Sometimes such a transaction is described as having aninterest rate of 12 percent per annum. More precisely, this rateshould be described as a nominal 12 percent per annum coumpoundedmonthly. |
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Clearly, it isdesirable to recognize the difference between 1 percent per monthcompounded monthly and 12 percent per annum compounded annually. If$1,000 is borrowed with interest at 1 percent per month compoundedmonthly, the amount due in one year is: |
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F =$1,000(1.01)12 = $1,000(1.1268) = $1,126.80 Thiscompares to F = $1,000(1+.12) =$1,120.00 for annualcompounding. |
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Hence, themonthly compounding has the same effect on the year-end amount dueas the charging of a rate of 12.68 percent compounded annually.12.68 percent is referred to as the effective interestrate. |
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To generalize, ifinterest is compounded m times a year at an interest rate of r/mper compounding period. Then, |
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The nominalinterest rate per annum, or the APR = m(r/m) = r. |
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The effectiveinterest rate per annum,or the EAR = (1+r/m)m - 1. |
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Consider a$100,000, 30 year, fixed-rate, 9 percent, home mortgage requiringmonthly payments. |
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a. The monthlyinterest rate on the mortgage is 9%/12 months = .75%. What is theAPR on the mortgage? |
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b. What is theEAR on the mortgage? |
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c. The borrower's payment book will look something like thefollowing. Complete the entries for the first 6 month. |
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Outstanding Balance Beginningof Month |
Monthly payment |
Interest due |
Principal payment |
Outstanding Balance End ofMonth |
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Date |
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01-31 |
$100,000 |
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02-28 |
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03-31 |
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04-30 |
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05-31 |
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06-30 |
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