# Future Value of a single Amount

Suppose you invest Rs 1,000 for three years in a savings account that pays 10 percent interest per year. If you let your interest income be reinvested your investment will grow as follows:

First Year: Principal at the beginning 1000
Interest for the year 100
(Rs 1000 x 0.10)
Principal at the end 1,100
Second year: Principal at the beginning 1,100
Interest for the year 110
(Rs 1,100 x 0.10)
Principal at the end 1,210
Third Year: Principal at the beginning 1,210
Interest for the year 121
(Rs 1,210 x 0.10)
Principal at the end 1,331

Formula

The process of investing money as well as reinvesting the interest earned thereon is called compounding. The future value or compounded value of an investment after n years when the interest rate is r percent is:

FVn = PV (1 + r) n —————eq ( 1)

In this equation (1 + r) n is called the future value interest factor or simply the future value factor.

To solve future value problems you have to find the future value factors. You can do it in different ways. In the example given above, you can multiply 1.10 by itself three times or more generally (1 + r) by itself n times. This becomes tedious when the period of investment is long.

Fortunately, you have an easy way to get the future value factor. Most calculators have a key labeled “yx”. So all that you have to do is to enter 1.10, press the key labeled y x enter 3 and press the“=” key to obtain the answer.

Alternatively, you can consult a future value interest factor (FVIF) table. Exhibit presents one such table showing the future value factors or certain combinations of periods and interest rates. A more comprehensive table is given in Appendix A at the end of the book.

Suppose you deposit Rs 1,000 today in a bank pays 10 percent interest compounded annually, how much will the deposit grow to after 8 years and 12 years?

Rs 1,000 (1.10) 8 = Rs 1000 ( 2.144)

= Rs 2,144.

The future value, 12 years hence will be:

Rs 1000 (1.10) 12 = Rs 1,000 (3.138)

= Rs 3,138

Value of FVIFr n for Various Combinations of r and n

n/r 6% 8% 10% 12% 14%

2 1.124 1.166 1.210 1.254 1.300
4 1.262 1.360 1.464 1.574 1.689
6 1.419 1.587 1.772 1.974 2.195
8 1.594 1.851 2.144 2.476 1.853
10 1.791 2.159 2.594 3.106 3.707
12 2.012 2.518 3.138 3.896 4.817

While tables are easy to use they have a limitation as they contain values only for a small number of interest rates. So often you may have to use a calculator.

Graphic View:

Exhibit above shows graphically how one rupee would grow over time for different interest rates. Naturally the higher the interest rates, the faster the growth rate. We can plot the growth curves for three interest rates: 0 percent, 6 percent, and 12 percent. Growth curves be readily plotted for other interest rates.

Compound and Simple Interest:

So far we assumed that money is invested at compound interest which means that each interest payment is reinvested to earn further interest in future periods. By contrast, if no interest is earned on interest the investment earns only simple interest. In such a case the investment grows as follows:

Future value = Present value [1 + Number of years x Interest rate]

For example, an investment of Rs 1,000, if invested at 12 percent simple interest rate will in 5 years time become:

1,000 [ 1 + 5 x 0.12] = Rs 1,600.

Exhibit below shows how an investment of Rs 1,000 grows over time under simple interest as well as compound interest when the interest rate is 12 percent. From this Value of Rs 100 Invested at 10 percent simple and compound Interest

Simple Interest:

Year Starting + Interest = Ending Balance
Balance

1 1000 + 100 = 1100
5 1400 + 100 = 1500
10 1900 + 100 = 2000
20 2900 + 100 = 3000
50 5900 + 100 = 6000
100 10, 900 + 100 =11000

Compound Interest:

Year Starting balance + Interest = ending Balance

1 1000 + 100 = 1100
5 1464 + 146 = 1610
10 2358 + 236 = 2594
20 6116 + 612 = 6728
50 106, 718 + 10672 = 117, 390
100 12, 527, 829 + 1,252,783 = 13, 780, 612

Exhibit you can feel the power of compound interest. As Albert Einstein once remarked: I don’t know what the seven wonders of the world are, but I know the eighth – compound interest. You may be wondering why your ancestors did not display foresight. Hopefully, you will show concern for your posterity.