Jon has 5,000 to invest in a savings account that has interest compounded annually . if he wants his money to double in eight years , what percent must the interest rate be on the account ?

9.1%

Step-by-step explanation:

Use the compound amount formula:

A = P(1 + r/n)^(nt), where P is the principal ($5000), r is the interest rate as a decimal fraction and is to be determined; n is the number of compounding periods per year (1 in this case), and t is the number of years.

Here we have A = double P = 2P =P(1+r/1)^(1*8), or

                                                  2   = (1+r)^8

We solve this for r by taking the natural logarithm of both sides:

                                                 ln 2 = 8*ln(1+r), or (after dividing both sides by 8)

                                                  ln 2

                                                  = ln (1+r)

                                                      8

                                                   0.6931

Since ln 2 = 0.6931, we have   = 0.0866 = ln (1+r)

                                                        8

Raise the base e to the power 0.0866 on the left side and raise the base e to the power ln (1+r) on the right side, obtaining:

1.091 = 1 + r

Subtracting 1 from both sides yields the desired value of r:

0.091 = r

The interest rate must be 9.1% for Jon's $5000 to double in eight years.