Question

Victoria is considering investing in an annuity being offered by Hopin Investments Ltd. The annuity will pay her $10,000 per half year for 4 years. Victoria 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 6.6% per annum, compounding monthly. What is the value of this annuity to Victoria?

Select one:

a. $67.994.10

b. $68,841.63

c. $70,101.87

d. $69,184.36`

Answer 1

Annuity will pay $10,000 per half year.

Nominla interest earned = 6.6% compounded monthly

First, we will convert Monthly compounding into semi- annual Interest rate:-

Half year Interest rate

where, r = Nominal Inrterest rate = 6.6%

m= No of times compounding in a year = 12 months (being monthly compounding)

n = no of periods = 6 months (Half-year Interest rate)

Half year Interest rate

Half year Interest rate = 1.03345709 - 1

=3.345709%

So, Half yearly interest rate = 3.345709%

Now, Calculating the Present Value of Annuity:-

Where, C= Periodic Payments =$10,000

r = Periodic Interest rate =3.345709%

n= no of periods = 4 years*2 = 8

Present Value = $69,184.36

So, the value of this annuity to Victoria is $69,184.36

Hence, Option D