Question

Suppose the interest rate is 8% APR with monthly compounding. What is the present value o an annuity that pays $90 every 6 months for 5 years?

Answer 1

This question is harder than it seems.

The problem is that the payment period does not coincide with the interest period.
So I will convert the 8% compounded monthly to a rate compounded semi-annually

let the semiannual rate be j
(1+j)^2 = (1.02)^4
1+j = (1.02)^2 = 1.0404
j = .0404

PV = 90(1 - 1.0404^-30)/.0404
= $ 1548.75

Answer 2

0.08/12 = 0.0066 or 0.66%

PV= 90/0.0066 (1-1/1.0066¹⁰) = $868.17