Question

Alexandrina is considering investing in an annuity being offered by Tamu Investments Ltd. The annuity will pay her $7,500 per half year for 6 years. Alexandrina 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 6.4% per annum, compounding quarterly. What is the value of this annuity to Alexandrina?

Select one:

a. $74,748.45

b. $72,124.55

c. $73,659.56

d. $71,328.97

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+(0.064/4)}^4]-1 = 0.065552 = 6.5552%

Therefore, For Semi Annual Rate,

0.065552 = [(1+i)^2]-1

1.065552 = (1+i)^2

i = (1.065552^1/2)-1 = 0.032256 = 3.2256%

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

Where, P = Annuity = 7500, i = Interest Rate = 0.032256, n = Number of Periods = 6*2 = 12

PV = 7500*[1-{(1+0.032256)^-12}]/0.032256 = 7500*0.316795/0.032256 = $73659.56