Compound interest - Math Central

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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

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