Question

Kerry Wate Plans to retire in exactly 10 years time, and he has a plan to create a fund that will allow him to receive $10,000 at the end of each year for the 20 years between retirement and death (a psychic has told him that he would die after 20 years). He is also been advised that he will be able to earn 7.5% interest per year during the retirement period.

1. How large a fund will Kerry need when he retire in 10 years time to provide the 20-year, $10,000 retirement annuity?
2. How much will Kerry need today as a single amount to provide the fund calculated in part (a) if he will earn only 5% interest per year during the 10 years preceding retirement?
3. What effect would an increase in the interest rate Kerry can earn both during and prior to retirement have on the values found in parts (a) and (b)? Explain.

Answer 1

a]	The fund should have a value equal to the PV of the
	annuity of $10,000 for 20 years discounted at 7.5%.
	Using the formula for finding PV of annuity, the amount to be had in the fund = 10000*(1.075^20-1)/(0.075*1.075^20) =	$       101,945
	[The formula for finding PV of annuity = Annuity*[(1+r)^n-1]/[r*(1+r)^n]
	where r = interest rate and n = number of years].
b]	Single amount [PV] to be deposited today = 101945/1.05^10 =	$         62,585
	[FV = PV*(1+r)^n, so PV = FV/(1+r)^n
	The amount of $101,945 is the future value and the amount to be
	deposited is the present value.
c]	An increase in interest rates would reduce the amounts
	in [a] and [c].