You have just deposited $10,000 into an account that promises to pay you an annual interest rate of 6.3 percent each year for the next 4 years. You will leave the money invested in the account and 10 years from today, you need to have $32,800 in the account. What annual interest rate must you earn over the last 6 years to accomplish this goal

The annual interest rate you must earn over the last 6 years to accomplish this goal is 17.03%.

Explanation:

Future value after 4 years = Deposited amount * (100% + Annual interest rate for 4 years)^4 = $10,000 * (100% + 6.3%)^4 =  12,768.30

The interest rate can be calculated using the following RATE function in Excel:

Interest rate = RATE(nper,pmt,-pv,fv,type) (1)

Where;

nper = number of periods = number of years remaining after 4 years = 10 - 4 = 6

pmt = Annual payments = 0 (This is 0 because there is no annual payment)

pv = present value = Future value after 4 years = $12,768.30

fv = future value = The amount you need to have in the account after 10 years = $32,800

type = when payments are due (0 = end of period. 1 = beginning of period) = 0

Substituting the values into equation (1), we have:

Interest rate = RATE(6,0,-12768.30,32800,0) (2)

Inputting =RATE(6,0,-12768.30,32800,0) into a cell in an excel sheet (Note: as done in the attached excel file), the annual interest rate is obtained as 17.03%.

Therefore, the annual interest rate you must earn over the last 6 years to accomplish this goal is 17.03%.