Home / Questions / In many financialtransactions, interest is computed and charged more than once ayear. Inte
In many financialtransactions, interest is computed and charged more than once ayear. Interest on corporate bonds, for example, is usually payableevery six months. 

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. 

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: 

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. 












Hence, themonthly compounding has the same effect on the yearend amount dueas the charging of a rate of 12.68 percent compounded annually.12.68 percent is referred to as the effective interestrate. 

To generalize, ifinterest is compounded m times a year at an interest rate of r/mper compounding period. Then, 

The nominalinterest rate per annum, or the APR = m(r/m) = r. 

The effectiveinterest rate per annum,or the EAR = (1+r/m)^{m}  1. 

Consider a$100,000, 30 year, fixedrate, 9 percent, home mortgage requiringmonthly payments. 













a. The monthlyinterest rate on the mortgage is 9%/12 months = .75%. What is theAPR on the mortgage? 

b. What is theEAR on the mortgage? 

c. The borrower's payment book will look something like thefollowing. Complete the entries for the first 6 month. 









Outstanding Balance Beginningof Month 
Monthly payment 
Interest due 
Principal payment 
Outstanding Balance End ofMonth 
Date 

0131 
$100,000 




0228 





0331 





0430 





0531 





0630 





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