Answer to Question #233209 in Financial Math for Nikka

Question

The present value of an annuity for three years is 5000, the payments are made at the end of every six months, and the interest rate is 6% compounded monthly. How large is each payment?

Answer 1

$FV=5000 \\ i=0.06 \times 6 = 0.36 \; \% \; per \;one \; period \\ n=3 \times 2=6 \\ FV = C \times [\frac{1-(1+i)^{-n}}{i}] \\ C= \frac{FV}{[\frac{1-(1+i)^{-n}}{i}]} \\ = \frac{5000}{\frac{1- (1+0.36)^{-6}}{0.36}} \\ = \frac{5000}{2.338} \\ =2137.86$

Each payment is 2137.86