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 Go to Math Central