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**Diamondlance** I'm studying for actuarial exam FM/2, and want to verify my calculations with someone. The problem is as follows: "Jerry will make deposits of 450 at the end of each quarter for 10 years. At the end of 15 years, Jerry will use the fund to make annual payments of Y at the beginning of each year for 4 years, after which the fund is exhausted. The effective annual rate of interest is 7%. Determine Y".

I first found the equivalent quarterly rate of interest to be 0.017058525 (since $\displaystyle 1.017058525^4=1.07$). Then $\displaystyle 450\displaystyle\frac{1.07^{40}-1}{0.07}=25512.23$ is the amount in the account after 10 years.

Multiplying that by $\displaystyle 1.07^5$ I got 35783.62. This is then equal to the value of the withdrawals at time 15, so $\displaystyle 35783.62=1.07Y\displaystyle\frac{1-1.07^{-4}}{0.07}$, and solving this gave me Y=9873.21.

The answer in the back of the book is 9872, which seems a bit far off for roundoff. Even so, I experimented with different reasonable intermediate round offs and couldn't get 9872...the fluctuations for reasonable round offs were only on the order of a few cents. Did I do something wrong? Any help would be appreciated.