Question

Kate Bwalya wishes to retire in 30 years’ time and has estimated that she will require a monthly pension income of K24,000 per month for 20 years subsequent to retirement. Kate will contribute to a retirement fund which will enable her to take out a monthly pension of K24,000 after retirement. The retirement fund is currently earning a return of 9% per annum, interest compounded monthly, and this level is expected to remain unchanged and to be sustainable over the next 50 years. Determine the monthly contribution that Kate is required to make to the retirement fund over the next 30 years.

Answer 1

1]	The first step is to find the amount that should be
	available at the beginning of the 31st year from now or
	at the end of the 30th year, so that a pension of K24000
	can be received monthly for 20 years, the first pension
	payment starting from the end of the 1st month after
	the 30th year.
	The amount required is the PV of the 240 installments of
	K24000 each.
	=24000*((1+0.09/12)^240-1)/((0.09/12)*(1+0.09/12)^240) =	$   26,67,478.90
2]	The above amount would be future value of the 360
	monthly installments that kate would be depositing into
	the retirement fund.
	So,
	2667478.90 = A*((1+0.09/12)^360-1)/(0.09/12)
	where A = the monthly deposit to be made
	Therefore A = 2667478.90*(0.09/12)/((1+0.09/12)^360-1) =	$           1,457.05