Question

Part 1-- The process of discounting and compounding are related. Please explain this relationship.

Part 2--Suppose you were considering depositing your savings in one of three banks, all of which pay 5 percent interest. Bank A compounds annually and Bank B compounds semiannually. What bank would you chose? Please explain why?

Answer 1

1) The process of discounting and compounding are related.

Required rate of return is either used to find the present value of future cash flows or to find the future value of a series of cash flow. The process of finding the present value is known as discounting and the process of calculating future value is known as compounding. Hence, both the process is used to adjust the value of money over a given period. Both uses the concept of time value of money, which states that an amount of money today is more of a worth than the same amount of money in the future. Compounding is therefore as discussed is used to calculate the worth of cash flows now in the future whereas, discounting is the process of finding out the worth of a stream of cash f,lows today. Value of money today will be less than that in the future making the worth of a dollar amount more today than in the future. Thus , both discounting and compounding are related as both works on the concept of time value of money and is used to find of the value of 1 dollar in present or future terms.

2) Bank B should be chosen, this is because more the compounding, greater is the effective annual interest rate. Effective annual interest rate is calculated as follows:

EAR = ( 1 + i/m )^m - 1

EAR = ( 1 + 0.05/2)² - 1

EAR = ( 1+ 0.025)² - 1

EAR = 1.050625 - 1

EAR = 0.050625

EAR = 5.0625%

Effective annual rate is 5.0625% for a semiannual compounding whereas for annual compounding it remains as 5.00%. Thus, Bank B is paying higher rate of interest as compared to Bank A and hence Bank B should be chosen.