Question

An investment pays $31.63 at the start of every quarter for 6 years.

a) how much should you pay for the investment if your required rate of return is 4.25% monthly compounding?

Answer 1

Given that,

PMT = $31.63 will be received at the start of every quarter for next 6 years

interest rate = 4.25% compounded monthly

So, first we need to calculate quarterly compounded rate,

So, effective annual rate = (1+APR/n)^n - 1 = (1+0.0425/12)^12 - 1 = 4.33%

So, quarterly compounded rate r = n*(((1+EAR)^(1/n)) - 1) = 4*(((1+0.0433)^(1/4)) - 1) = 4.27%

So, present value of annuity is calculated using formula

Present value = PMT*(1+r/n)*(1 - (1+r/n)^(-n*t))/(r/n) = 31.63*(1+0.0427/4)*(1-(1+0.0427/4)^(4*6))/(0.0427/4) = $673.77

So, cost of the investment today is $673.77