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Different compounding periods, are used for different types of investments. In order to properly compare investments or loans with different compounding periods, we need to put them on a common basis. In order to do this, you need to understand the difference between the nominal interest rate (INOM) and the effective annual rate (EAR). The nominal interest rate is quoted by borrowers and lenders, and it is also called the annual percentage rate (APR). If the compounding periods for different securities is the same, then you can use the APR for comparison. If the securities have different compounding periods, then the EAR must be used for comparison. Here, M is the number of compounding periods per year and INOM/M is equal to the periodic rate (IPER). If a loan or investment uses annual compounding, then the nominal interest rate is also its effective annual rate. However, if compounding occurs more than once a year, EAR is equal to INOM. Quantitative Problem: Bank 1 lends funds at a nominal rate of 10% with payments to be made semiannually. Bank 2 requires payments to be made quarterly. If Bank 2 would like to charge the same effective annual rate as Bank 1, what nominal interest rate will they charge their customers? Do not round intermediate calculations. Round your answer to three decimal places. An important application of -Select- interest involves amortized loans. Some common types of amortized loans are automobile loans, home mortgage loans, and business loans. Each loan payment consists of interest and repayment of principal. This breakdown is often developed in an amortization schedule. Interest is -Select- in the first period and -Select- over the life of the loan, while the principal repayment is -Select- in the first period and it -Select- thereafter. Quantitative Problem: You need $10,000 to purchase a used car. Your wealthy uncle is willing to lend you the money as an amortized loan. He would like you to make annual payments for 5 years, with the first payment to be made one year from today. He requires a 7% annual return. a. What will be your annual loan payments? Do not round intermediate calculations. Round your answer to the nearest cent. b. How much of your first payment will be applied to interest and to principal repayment? Do not round intermediate calculations. Round your answers to the nearest cent. Interest: $ Principal repayment: $

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Answer:

The Nominal interest rate is quoted by borrowers and lenders, and it is also called the annual percentage rate (APR). If the compounding periods for different securities is the same, then you Must Be use the APR for comparison. If the securities have different compounding periods, then the Effective annual rate must be used for comparison. Here, M is the number of compounding periods per year and INOM/M is equal to the periodic rate (IPER). If a loan or investment uses annual compounding, then the nominal annual rate is also its effective annual rate. However, if compounding occurs more than once a year, EAR is Use as INOM. Effective annual rate for bank 1 = [(1 + 10%/2)^2] - 1 = 1.1025 - 1 = 10.25%. Effective annual rate for bank 1 is = 10.25%. If Bank 2 would like to charge the same effective annual rate as Bank 1, but Bank 2 charge quarterly compounding interest rate. Nominal Rate of bank 2 = [( 1 + 10.25%)^(1/4) - 1] x 4 = 9.878%

Second question: 1. Compound 2. Largest, declines 3. Smallest, increases PV=10000 I/Y=9% N=4 CPT PMT-2,438.91 Interest=10000*7%=700 Principal=2,438.91-700=1738.91|