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