Question

You have a trust fund that was set up by your great uncle which will pay you $40,000 on your 40th birthday and $10,000 on your 50th birthday. Assume that once you receive these two payments you can also invest then at a nominal rate of 5.5% to increase your retirement savings. Assume you still want all of your retirement savings contributions to be a constant annual nominal amount (an annuity). Calculate the amount you will now need to save each year until you retire if you start saving next year on your 31st birthday.

Answer 1

Given,

On 40th Birthday,

Amount you will receive = $40,000

On 50th Birthday,

Amount you will receive = $10,000

Nominal Rate = 5.5%

In order to contribute for Retirement savings from 31st birthday, Amount of annual contribution shall be as follows:

At present on 30th Birthday

Present value of amount received on 40th Birthday

= 40,000×PVF(5.5%, 10)

= 40,000×0.5854

= 23,416

Present value of amount received on 50th Birthday

= 10,000×PVF(5.5%,20)

= 10,000×0.3427

= 3,427

Total present value as on 30th Birthday

= 23,416+3,427 = 26,843

Amount of annual contribution for retirement savings from next year ie., from 31st Birthday

= 26,843÷PVAF(5.5%,20)

= 26,843÷11.9504

= $2,246