   SEARCH HOME Math Central Quandaries & Queries  Question from Kenneth: Hello: Let's say that an investor has $1000.00 to invest for 3 years at a rate of 5% at compound interest. Here is the formula: M = 1000(1 + 0.05)^3 =$1157.62 If I want to change 1000(1 + 0.05) to (1000 + 0.05*1000) three times in a calculation instead of using (1 +0.05)^3, how would this be done? I cannot get (1000 + 0.05*1000) + (1000 + 0.05*1000) + (1000 + 0.05*1000) to equal $1157.62. I know that 1000(1.05)(1.05(1.05) will produce the answer, but I want to try to use the above non-factored calculation. I thank you for your reply. Kenneth, If you invest$1000 for 1 year at 5% then at the end of the year you have $(1000 + 0.05*1000). Your calculation of (1000 + 0.05*1000) + (1000 + 0.05*1000) + (1000 + 0.05*1000) is the result of making 3 investments of$1000 each, at 5% for 1 year.

The compound interest calculation you mention

1000(1 + 0.05)3 = $1157.62 is the result of investing$1000, once for three years at 5%, compounded annually. At the end of the first year you have

$(1000 + 0.05*1000) =$1050.

"Compounding" means that this amount is reinvested at 5% and hence at the end of the second year you have

$1050 + 0.05 *$1050 = $1102.50. Compounding again for year three gives you$1102.50 + 0.05 *$1102.50 =$1157.625.

Rather than perform these three calculations you can perform the one calculation

1000(1 + 0.05)3.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.