Suppose $500 is compounded annually for 14 years. If no other deposits are made, what rate is needed for the balance to triple in that time?

Answer 1

Since this is a simple interest problem, we can use the slightly modified formula for compound interest to find the rate. We'll see up the equation in the form of A = P ( 1 + r )ⁿ where A is the final amount, P is the initial deposit, r is the interest rate, and n is the number of years. So it will look like this: 1500 = 500( 1 + r) ¹⁴.

Dividing both sides by 500, we have 3 = ( 1 + r )¹⁴. If we raise both sides to the power of 1/14, this will isolate the (1 + r ), and the other side of the equation where we have 3^(1/14) becomes 1.08163. So now the equation becomes 1.08163 = 1 + r. Subtracting one from both sides, we see that r =.08163. If we convert to a percent, we see that the rate is approximately 8%.