Suppose $1,000 is compounded quarterly for 4 years. what rate is needed to reach a total of $1,500? round to the nearest tenth of a percent.

10.3% compounded quarterly. The formula for compound interest is A = P (1+I/N) ^TN where A = Amount after interest is granted P = Principle I = Interest rate N = Number of periods per year T = Number of year Since we want to get 1500 with an starting principle of 1000, that means that (1+I/N) ^TN has to equal 1.5. And since we know that TN will be 4 * 4 or 16, we know that (1+I/N) has to be the 16th root of 1.5, so let's calculate 10^ (log (1.5) / 16) = 10^ (0.176091259/16) = 10^0.011005704 = 1.025665396 Now write the expression 1 + I/4 = 1.025665396 And solve for I 1 + I/4 = 1.025665396 I/4 = 0.025665396 I = 0.102661586 So the desired interest rate will be 10.3% compounded quarterly.