Question

Luke and Amy are saving for the down payment on a house. The houses in the area they prefer have an average selling price of $450,000 and they need a 10% down payment to ensure their mortgage payments are not too high. They have $30,000 saved that they can invest today at 6.5% (annual compounding).

a) How long before they will have enough for the down payment saved?

b) They want to buy the house sooner.  In addition to the $30,000 saved to date, how much would they need to invest each month (into the same investment) in order to have enough for the down payment in 2 years?

c) What would their payments be for part (b) if they made them at the beginning of the month instead of the end?

Answer 1

Required Down payment=450000*10%=$45000

a) To get the required down payment FV=45000, rate=6.5%, PV= 30000, nper=?

So, they will have down payment at the end of 6.43 year or 7 year (As interest rate is annual compounding and interest is paid at the end of the year)

b) Say, the equivalent monthly rate of return is x

Then, (1+x)^12-1=6.5%

or, x= (1+6.5%)^(1/12)-1=0.526%

So, in this case nper=2*12=24 months, rate=0.526%, PV=-30000, FV=45000, PMT=?

Hence, they should invest additional $430.16 into the account in order to have enough for the down payment in 2 years.

c)

Similarly,

So, their payments be for part (b) if they made them at the beginning of the month instead of the end would be $427.91