Question

Silva is contemplating to buy a 20 year annuity paying $2500 at the end of each month. What amount will be required to purchase the annuity, if the annuity provides a return of 6.75% compounded annually?

Answer 1

Given that,

20 year annuity paying $2500 at the end of each month

So, monthly payment PMT = $2500

years of payment t = 20 years

interest rate = 6.75% compounded annually,

So, first calculating APR compounded monthly,

So, APR = n*((1+EAR)^(1/n) - 1) = 12*(1.0675^(1/12) - 1) = 6.55%

So, amount today PV, can be calculated using Present value formula of ordinary annuity,

PV = PMT*(1 - (1+APR/n)^(-n*t))/(APR/n) = 2500*(1 - (1+0.0655/12)^(-12*20))/(0.0655/12) = $333998.96

So, amount required to purchase the annuity = $333999