# Semi Annual Deposit Compounded Quarterly

A son planned to endow 1000000 to his son on his son's 21st birtthday. How much is his semi-annual deposit in a special account that earns 5% compounded quarterly if the first deposit was made when the son was 4.5 years old?

I used the future worth of annuity:

F = A( ((1+i)^n - 1) / i)
F = 1000000
i = 0.05/4
n = 21-4.5 years = 16.5; 16.5*2 = 33 (semi annual)

I get A = 24667.86 What am I doing wrong?

If you want to do it with calculation then you've got to think in terms of payment periods. So the first period starts at his 4th birthday, and the first payment is made at 4.5. So ($(21-4)*2=34$).