# Thread: Future value annuities with a different payment period to the compounding period.

1. ## Future value annuities with a different payment period to the compounding period.

I have a question in the extended modelling part of my text book to do with annuities that have a repayment period and compounding period that are not equal. The exact question is below;

"A person deposited \$2000 into a bank account on his 21st birthday. He deposited the same amount on each succeeding birthday, the lat deposit being when he turned 54. He closed the account on his 60th birthday.
How much did he receive if:
i) Interest has been at a rate of 8% p.a, compounded annually
ii) Interest has been at a rate of 8% p.a, compounded monthly."

As I understand it this messes up the equation for future value annuities as the compounding and repayment period must be equal for it to work.

I was thinking that the only way to do this would be with a spreadsheet, however is there an equation? If not what would I need to do in the spreadsheet to make sure I am getting right?

Thank you very much!

2. Yes, there is an equation. Work out the accumulated value of the fund at the date of last payment, then grow it with interest until his 60th birthday.

3. I found the solution finally, rahter simple and elegant in the end. Convert the monthly interest rate (0.08/12) to an annual interest rate by doing this ((0.08/12+1)^12)-1 = 0.083 and then use that in the FV formula with n=34 and then multiple the result from the FV formula by 1.083^6