Why docs the observed pattern of FVs occur? Time Value of Money: Comparing Inter

Question

Why docs the observed pattern of FVs occur? Time Value of Money: Comparing Interest Rates 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 pul 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 (FAR) The_interest rate is quoted by borrow ers and lenders, and it is also called the annual percentage rate (APR I- If the compounding periods for different securities is the same, then you_use the APR for comparison. If the securities have different compounding periods, then the_must be used for comparison. Here. M is the number of compounding periods per year and I_NOM/M equal to the periodic rate (I_pER). if a loan or investment uses_compounding. then the nominal annual rate is also its effective annual rate. However, if compounding occurs more than once a year. EAR is_Inom Quantitative Problem: Bank I 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 I. what nominal annual rate will they charge their customers? Round your answer to three decimal places. Do not round intermediate calculations._%

Explanation / Answer

"Nominal Interest Rate"

If securities have different compounding periods, then you "must" use the APR.

"Effective Interest Rate"

"Annual Compounding"

""Compounding Periods x "

Solution for Quantiative Problem:

Effective annual rate for Bank 1:

EAR = [1+(r/m)]m 1

Where, r and i are interest rates in decimal form. m is the number of compounding periods per year. The effective annual rate is the actual interest rate for a year

= > [1+(.10/2)]2 1 = 0.1025 or 10.25

So, Nominal interest rate required for Bank 2:

0.1025 = [1+(r/2)]2 1
= > 1.1025 = [1+(r/2)]2
= > r = 0.09878 or 9.878%

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