Question

Mark wants to save money to achieve three main objectives.

1º, he would like to be able to retire within 30 years with a retirement income of $23,000 per month for 20 years, with the first payment received 30 years and 1 month from now.

2º, he would like to buy a cabin in 10 years at an estimated cost of $320,000.

3º, after he dies at the end of the 20 year retirement period, he would like to leave a $1,000,000 inheritance to his nephew. Mark can save $2,100 per month (ordinary annuity) for the next 10 years.

In addition, Mark can obtain an effective annual return of 11 percent before retirement and an effective annual return of 8 percent after retirement.

(a) What is the amount of savings that Mark needs to have at the time of retirement?

(b) How much are Mark's savings immediately after buying the cabin?

(c) How much Mark will have to save each month (ordinary annuity contributions) after the purchase of the cabin (i.e. after the year 10 and until the year 30)?

Answer 1

a	Savings needed at time of retirement
	PV of Retirement Income	$2,749,748.71
	Present Value of inheritance	$214,548.21
	Savings needed at time of retirement	$2,964,296.92
b	Savings before buying the cabin	$455,696.09
	Savings after buying the cabin	$135,696.09
c	Value of savings after buying the cabin at retirement	$1,094,024.16
	Balance required	$1,870,272.76
	Amount to be saved each month	$2,160.57

WORKINGS