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Question

Turner and his wife are saving for a down payment on a house. They think that they need $75,000.

A. If Turner and his wife each put $100 from each paycheck (i.e.$200 weekly) into an account that pays 1.8% annual interest (compounded weekly) will they have enough money for the down payment in 7 years?

B. If Turner wants to have the $75,000 deposit in 7 years, but doesn't want to put aside any extra, how much money do he and his wife need to save together (weekly at 1.8% interest)?

Answer 1

A. PMT = $200 per week; r = 1.8% = 0.018, t = 7 years, n = 52 weeks per year

FV = PMT((1 + r/n)^nt - 1)/(r/n) = 200((1 + 0.018/52)^52·7/(0.018/52) = $77570.96 > $75000

So, they get enough money for down payment.

B. FV = 75000 we ned to get PMT everything the same data, then

PMT = FV(r/n)/[(1 + r/n)^nt - 1] = 75000(0.018/52)/[(1 + 0.018/52)^52·7 - 1] = $193.37 per week