Question

Ben Cunnington is planning for his retirement and has $50,000 to invest as a lump sum into a retirement investment plan. Ben plans to work for another 35 years before retiring at the age of 65 and, as well as the $50,000 lump sum, he plans to deposit $1,500 into a capital secured share index fund each month of his remaining working life. He estimates that his retirement account will generate an annual return of 7%. Ben plans to retire at 65 and then draw a pension from his savings for a further twenty five years. During this retirement phase Ben expects to be investing conservatively and estimates a 5% per annum return. At the age of 90, at the completion of the pension, Ben would like to have $200,000 remaining in the account for contingencies. (i) Calculate the Future Value of the monthly saving deposits and the lump sum deposited today based on monthly compounding and a rate of 7% per annum . (ii) Calculate the annual pension that Ben will receive after retirement, taking into account the requirement to have $200,000 remaining at the end of the pension period. Ben plans to receive his first retirement pension payment annually with the first payment occurring one year after he retires .

Answer 1

(i)	FV of the lumpsum compounded monthly = 50000*(1+0.07/12)^(35*12) =	$     5,75,307.59
	FV of the annuity of $1500 = 1500*((1+0.07/12)^420-1))/(0.07/12) =	$   27,01,581.90
	Total FV	$   32,76,889.49	Answer
(ii)	PV (as at the age of 65) of the amount of $200000 (to be had at 90 years of age) = 200000/((1+0.05/12)^300)) =	$         57,449.96
	Balance available for pension (3276889.49-57449.96)	$   32,19,439.53
	Annual pension receivable with the above amount (which is the PV of the pension, which is an annuity) = 3219439.53*((0.05/12)*(1+0.05/12)^300))/((1+0.05/12)^300-1)) =	$         18,820.52	Answer