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Find the present value of a ten-year annuity which pays $400$ at the beginning of each quarter

for the first $5$ years, increasing to $\$600$ per quarter thereafter. The annual effective rate of interest is $12\%$.

Answer to the nearest dollar.

I found the quarterly interest rate(j) to be $$ (1+j)^4 =(1.12) j=0.0287 $$

I tried drawing a time line to find the equation of value. I am not sure on how to write the formula I know i am suppose to use annuity due for present values However, what would $n$? $n$=the number of payments

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here check this out, the answer is in that link,i took a screenshot. – user85254 Jul 6 '13 at 17:47

$PV = 400\ddot{a}_{\overline{40|}j} + 200\ddot{a}_{\overline{20|}j}v^{20} \approx 400(24.27) + 200(15.48)(.567)=11463$

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