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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?

The answer is 16640.20

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?

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Well the first issue seems to be that there are in fact 34 payments. They've tripped you up by putting a payment at the beginning and at the end of the period.

Often with these I like to do a couple of smaller calculations. Eg how many payments by his fifth birthday (2). How many by his sixth (4). You can see the trend.

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 ($(21-4)*2=34$).

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