Question

 

1. Discuss how time value of money in the context of compounding interest.

2. Explain what an annuity is and what are the two most common types of annuity. Explain how the present value and future value of an annuity is determined.

3. Extend the notion of compounding mentioned in your answer to part “a” above to general situations where compounding is induced by growth, inflation, or deflation.

Answer 1

Compounding is basically reinvestment of profits earned from an investment at a certain interest rate. It might be the same interest rate as of the previous year or maybe different depends on the situation or the scenario.

In the case of inflation which is also called purchasing power parity, it changes every quarter or year which depends on the spending pattern of consumers and the availability of liquid cash in the economy. This decides the value of the money. There is a very famous quote that "Money today worth more than money tomorrow in an inflating economy". This means in time value of money that $100 today and tomorrow is not the same rather it should be discounted by the tomorrows inflation rate. The inflation rate is the rate at which the price of a commodity or goods increases. So if you could buy 10 apples today with $10 then you might not buy the same in the next quarter. You may be purchasing fewer apples or more depends on the inflation or deflation of the economy respectively.

So when we are calculating the value or worth of money inflation rate or deflation rate has to be considered. As this value changes over a period of time so individual rates have to be considered for a period of time let say annually or semi-annually or quarterly or monthly. These individual rates are then compounded rather than being added as they have an effect on each cash flows. Let say we are depositing a certain sum A annually into a fund. Then the inflation rate of every year has to be discounted in a compounded manner as it is applicable only to that year not for the previous year.

So, the value of the deposit will be = A/(1+i)^10 + A/(1+i)^9 + --------------- + A/(1+i)

In the growth, scenario let say when we are saying a company is growing its sales 5% every year which means the sales figure of the previous year has grown 5% this time and this figure will be growing again by 5% in upcoming year. This clearly states the effect of compounding or the increment value and the previous value both will be growing at 5%.

So we can conclude that the componding effect is induced by growth, inflation, deflation.