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