Question

You wish to retire in 12 years, at which time you want to have accumulated enough money to receive an annual annuity of $15,000 for 17 years after retirement. During the period before retirement you can earn 11 percent annually, while after retirement you can earn 13 percent on your money. What annual contributions to the retirement fund will allow you to receive the $15,000 annuity?

Answer 1

In first step, we will find out the present value (i.e.value at the start of retirement) of annuity payment $15000 for 17 years (Interest rate 13% p.a.)

In second step , we will find out the annual contribution required for 12 years (i.e.till retirement) to arive at value calculated in step 1 (Interest rate is 11% p.a.)

Step 1

We can use the present value of annuity formula to calculate this value.

Present value of annuity = P x {[1 - (1+r)^-n]/r}

Present value of annuity =   present value (i.e.value at the start of retirement) of annuity payment $15000 for 17 years = ?

P = annuity payment = $15000

r = rate of interest after retirement = 13%

n = number of years = 17

Present value of annuity = 15000 x {[1 - (1+0.13)^-17]/0.13}

Present value of annuity = 15000 x 6.729093

Present value of annuity = 100936.39

Present value (i.e.value at the start of retirement) of annuity payment $15000 for 17 years = $1,00,936.39

Step 2

We can use the future value of annuity formula to arrive at annual contribution required for 12 years to get value calculated in step 1.

Future value of annuity = P x {[(1+r)^n -1]/r}

Future value of annuity = value calculated in step 1 = $100936.39

P = annual contribution required = ?

r = rate of return = 11% p.a.

n = number of years left for retirement = 12

100936.39 = P x {[(1+0.11)^12 -1]/0.11}

100936.39 = P x 22.71319

P = 4443.96

Annual contribution required for retirement fund = $4,443.96