Saturday, March 22, 2008

Compounding interest formula

Money grows exponentially with the compounding of interests!

Just imagine, you put in $2,000 in a bank account which has a fixed interest rate of 3% and when the interest on this $2,000 has accrued at the end of the year, instead of taking out the interest, you plough back this interest of $60 to the $2,000 that you have placed at the beginning of the earlier year to reap an even bigger interest.

Thus, at the beginning of the second year, you would have $2,060 in your account for the interest to effect on in the second year, and so on subsequently.

I have provided below a useful formula for the calculation of the amount one can receive in the nth year due to such compounding of interest:

Amount received in nth year= {(1+ rate of compound interest) to the power of n} multiply by starting amount put in Year 1, e.g. if interest rate is 15%, rate of compound interest = 0.15)

There is another form of compounding of interest rate. Say you put $300 every month into a bank deposit and at the end of every year; there will be an x % of interest earned on the amount accumulated at the end of each year. Instead of taking out this interest, you keep this interest earned so that the interest earned on the 2nd year will be on the amount you have accumulated over the past two years together with the interest.

It will be clearer with an example.

Assume you put in $300 per month into a bank account with a compound interest of 15%. At the end of the first year, you would have $3,600 and with the 15% interest earned on this amount you would have $4140. Similarly, at the end of the second year, you would have amassed ($4,140 +$3,600) x 1.15= $8,901

Let x =monthly amount put in the account
n = number of years
y = interest rate (e.g. if interest rate is 15%, y= 0.15)

The general calculation would be as follows:

1) 12 multiply by x multiply by (1+y)
2) Divide the result obtained in 1) by y
3) Calculate (1+y) to the power of n, then minus 1 from this result
4) Multiply the result obtained in 2) with that obtained in 3) to obtain the amount amassed at the end of nth year due to the compounding of interest.

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