Monday, May 12, 2008

The Power of Compounding

Let me ask you a question, if you won a cash prize and you are given the following payment options:
a. Received $10,000 now
b. Receive $10,000 in three years
Which option will you choose? The answer will be ‘a’ if you understand the time value of money. Receive $10,000 today allow you to increase the value of the money by investing and gaining interest out of it. As for option b, you may lose the opportunity to create the increase because you are only been promised the future value of $10,000. This is known as Time Value.

Future Value (FV)
If you choose option ‘a’ and decided to invest the money at annual rate of 5%, your return value at the end of one year will be $10,500. How to calculate this future value?
The equation to calculate the return is
= ($10,000 * 5%) + $10,000 = $10,500

Rearrange this equation and you get
= $10,000 (1 + 5%) = $10,500

Future value = Present value (or original value) * (1 + interest rate)

If you continue to leave your money in that investment for another year, your return value at the end of two years will be $11,025. To calculate this,
Future value = $10,500 * (1+0.05) = $11,025
This is the same as rewriting equation as
$10,000 * (1+0.05) * (1+0.05) = $11,025

Now, think back to your math class, you can rewrite multiplication of similar terms by adding their exponents
Future value = $10,000 * (1+0.05)(1+1) = $10,000 * (1+0.05)(2)

You can continue to calculate future value for 3years, 5years etc using the following future value equation.

Future value = Present value * (1 + interest rate per period)^(Number of periods)

Similarly, you can use Microsoft Office Excel equation to perform you calculation. Open a new excel document, click on ‘insert function’ (fx) button and look for ‘FV’ under financial category.

FV(rate,nper,pmt,pv,type) – returns the future value of an investment based on periodic, constant payments and a constant interest rate. The equation is very self explainable.
Rate is the interest rate per period
Nper is the total number of payment periods in the investment
Pmt is payment made each period; it cannot change over the life of the investment
Pv is the present value, or the lump-sum amount that a series of future payments is worth now, If omitted, Pv = 0
Type is a value representing the timing of payment: payment at the beginning of the period = 1; payment at the end of the period = 0 or omitted

For this above example, to calculate future value for 2 years, you will enter value as FV(0.05,2,0,-10000,0); and you will get the similar answer of $11,025. Note that you have to set -10000 which represent the outflow of your money.

Compound Interest
Take another step future, imagine you have opportunity to invest your money at same interest rate of 5% for longer period of time (e.g. 10, 20, 30 or 60 years, etc). How much is your return will be? What is it like if you can invest with higher interest rates (e.g.10%, 15% or 20%)? Look at the following table

Look at the return for 20% interest rate. This is what the power of compounding interest can do for you if you choose to use it smartly by selecting the appropriate interest rate versus number of periods. Someone had said that the power of compounding was deemed the eighth wonder of the word.

1 comment:

gummy bear said...

Would it be better to show this idea using the number of compounding per year against the Year with the same interest rate?