Time Value of Money, Part-3

How to use future value and present value concepts when compounding is not annual?

Let’s first of all understand the concept of simple interest and compound interest.

Simple Interest:

I invested Rs.100 for 3 years at simple interest of 10% per annum.

In this case interest = 100×10% = Rs.10

So Rs.10 will be paid over a period of 3 years and Rs.100 will be paid back as maturity value.

Year	Amt Rs.
1	10
2	10
3	10+100

Now instead, I invested Rs.100 for 3 years at compound interest of 10% per annum

There will be no intermittent cash inflows to me and whatever interest is accrued will be reinvested at 10% and I will get a lump sum at the end of 3 years.

Year	Amt Rs. at the end of year
1	100+10(interest @10%) = 110
2	110+11(interest @10%) = 121
3	121+12.1(interest @10%) = 133.1

Hence I will get Rs.133.1 at the end of 3 years. This is the concept of compound interest and it differs from simple interest. Practically majority of the investment products follow the concept of compound interest. Normally compounding can be made on monthly/quarterly/semi-annually/annual basis.

Semi-annual compounding:

Mr. A invested Rs.1000 in National Saving Certificate. Maturity is 6 years and rate of interest is 8% compounded semi-annually. What amount he will receive at maturity?

Solution:

PV = -1000

i/y = 8/2 = 4 (as compounding is semi-annual)

N = 6×2 = 12 (as compounding is semi-annual)

FV = ?

Answer: Rs.1601

Quarterly compounding:

Mr. A invested Rs.1000 in bank fixed deposit. Maturity is 5 years and rate of interest is 8% compounded quarterly. What amount he will receive at maturity?

PV = -1000

i/y = 8/4 = 2 (as compounding is quarterly)

N = 5×4 = 20 (as compounding is quarterly)

FV = ?

Answer: Rs.1486.

Monthly Compounding:

Mr. A invested Rs.1000 in company fixed deposit. Maturity is 5 years and rate of interest is 12% compounded monthly. What amount he will receive at maturity?

PV = -1000

i/y = 12/12 = 1 (as compounding is monthly)

N = 5×12 = 60 (as compounding is monthly)

FV = ?

Answer: Rs.1817.

Note: Practice questions will be published soon.

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