Question

8. What is the fair market value for a retirement annuity that would provide $3000 at the end of each month at 5% compounded quarterly for the first 10 years and $3000 at the end of each month at 6% compounded quarterly for the following 5 years? (BUSINESS MATHS)

Answer 1

Solution:

We compute Present Value of Annuities.

1] Present value of Annuities of $3000 each month at 5% compounded quarterly for the first 10 years.

So quarterly payment = $9000

Quarterly compounding rate = 5%/4 = 1.25%

No fo quarters = 10*4 = 40

Present value of annuity = 9000/0.0125 *(1- 1/(1+0.0125)^40) = 281,942.4 ............[A]

2] Present value of Annuities of $3000 each month at 6% compounded quarterly for the next 5 years.

So quarterly payment = $9000

Quarterly compounding rate = 6%/4 = 1.5%

No fo quarters = 5*4 = 20

Present value of annuity = 9000/0.015 *(1- 1/(1+0.015)^20) = 154,517.7

Howevery, this value is after 10 years. So discounting it to todays value using 1.25% quaterly rate

= 154,517.7/(1+0.0125)^40 = 94,010.63 ..................... [B]

Fair Market Value of retirement annuity = A+B = 281,942.4 + 94,010.63 = $375,953.

-x-