A principal amount of $5,000 was invested in a savings account for 5 years.The interest earned was $500.Use the simple interest formula to find the annual rate of interest.

Hi,

If you invest $5,000 for one year at an interest rate of r [maybe 5% (r = 0.05) or 3% (r = 0.03)] then at the end of the year you have the amount invested [$5,000] plus the interest [r*$5,000]. That is at the end on one year you have

$5,000 + r*$5,000 = $5,000*(1+r) What you should see here is that the amount returned after one year is (the principle)*(1+r)

In the second year you are investing $5,000*(1+r) [this is the new principle] and hence the return at the end of the second year is

(the principle)*(1+r) = $5,000*(1+r)*(1+r) = $5,000*(1+r)2

Thus at the beginning of the third year the principle is $5,000*(1+r)2 and hence the return at the end of the third year is $5,000*(1+r)3

Continuing in this way the return after 5 years is

$5,000*(1+r)5

In your problem the interest after 5 years is $500 so the total return after 5 years is $5,000 + $500 = $5,500. Hence

$5,000*(1+r)5 = $5,500 Now you can solve for r.

$5,000*(1+r)5 = $5,500 Hence (1+r)5 = $5,500/$5,000 = 1.1 Take the fifth root of both sides to find 1+r and then solve for r.

Cheers,
Penny
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