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

Part I

The concept of time value of money says that worth of money keeps changind in future. The concept of time value includes two further sub-concepts: Present Value and Future Value. There are two methods used for ascertaining the worth of money at different points of time, namely, compounding and discounting. Compounding method is used to know the future value of present money and discounting is a way to compute the present value of future money.

If we calculate future value of a given money at a given compounding rate and then calculate present value by discounting (with same rate equals to compounding rate) then we will get the simlar amount as present value from which we have started.

In Short, Compounding is helpful to know the future values, of the cash flow, at the end of the particular period, at a definite rate while discounting is used to determine the present value of the future cash flow, at a certain interest rate.

Part 2

We will choose Bank B which compound interest semiannually. Because it will ends up with higher amount at the end with compare to the bank which compount interest annually. For e.g if we invest 10000 dollers in bank A then at the end of the year we wil have 10500 dollers. However in bank B we will have 10000*1.025*1.025 = 10506 dollers.