Question

Louise is considering investing in an annuity being offered by Pakokku Investments Ltd. The annuity will pay her $3,200 per quarter for 11 years. Louise is trying to work out how much this annuity is worth. She thinks she should receive a return equivalent to a nominal interest rate of 7.30% per annum, compounding daily. What is the value of this annuity to Louise? Select one:

a. $95,914.91 b. $93,354.85 c. $92,587.20 d. $97,256.03

Answer 1

Effective Interest Rate or EAR = [{1+(APR/n)}^n]-1

Where, APR = Annual Interest Rate or Nominal Rate, n = Number of times compounded in a year

Therefore,

EAR = [{1+(0.073/365)}^365]-1 = 0.0757 = 7.57%

Therefore, For Quarterly Rate,

0.0757 = [(1+i)^4]-1

1.0757 = (1+i)^4

i = (1.0757^1/4)-1 = 0.01841 = 1.841%

PV of Annuity = P*[1-{(1+i)^-n}]/i

Where, P = Annuity = 3200, i = Interest Rate = 0.01841, n = Number of Periods = 4*11 = 44

PV = 3200*[1-{(1+0.01841)^-44]/0.01841 = 3200*0.55187/0.01841 = $95925.41 which is equivalent to $95914.91