Question

If you deposit $500 from year 1 to year 5, $300 from year 6 to year 20, and no deposit in year 20 and 21, and $700 in year 22. If the discount rate is 5%, what is the present value?

Answer 1

We just need to arrange the cash flows in order and fro similar cash flows for a continuous period we can use the Annuity Factor of the discount rate.

So the Present value will be:

Period	Cash flows	Annuity Factor	Present Value (Cash Flow x Annuity Factor)
Year 1-5	$500	PVAF(5%,5) = 4.3295	2164.75
Year 6-20	$300	PVAF(5%,15) = 10.3797	3113.91. This will be again discounted for 5 years to bring it to today. So, 3113.91/(1.05^5). = 2439.83
Year 22	$700	PV factor (5%,22)	239.30

Therefore, total of all the present values is 2164.75 + 2439.83 + 239.30

= $4843.88.