Question

In the following ordinary annuity, the interest is compounded with each payment, and the payment is made at the end of the compounding period.

You and your new spouse each bring home $1500 each month after taxes and other payroll deductions. By living frugally, you intend to live on just one paycheck and save the other in a mutual fund yielding 7.86% compounded monthly. How long will it take to have enough for a 20% down payment on a $165,000 condo in the city? (Round your answer to two decimal places.)

Answer in YEARS

Answer 1

1]	Down payment required = 165000*20% =	$         33,000
2]	Now, $33,000 is the FV of the annuity [the monthly
	savings in MF] of $1500.
	Hence,
	33000 = 1500*FVIFA(0.655,n), where n = the number
	of months required to reach $33,000 and 0.655 is
	the monthly interest in % [7.86/12].
	Solving for n:
	FVIFA(0.655,n) = 22
	Using a financial calculator:
	For 0.655%, factor is 22.4343 for n = 21
	For 0.655%, factor is 21.2948 for n = 20
	Value of n, by simple interpolation = 20+(22-21.2948)/(22.4343-21.2948) =	20.62	Months
	In years = 20.62/12 =	1.72	Years
	VERIFICATION:
	FV = 1500*(1.00655^20.62-1)/0.00655 =	$   33,000.60