Question

A young graduate is saving for house on Lake Hartwell. The young graduate is planning on saving $1,135.00 each quarter for 10.00 years in an investment account paying 6.48% interest that is compounded quarterly. His first deposit will be made at the end of the next quarter, so this is a regular annuity. In 10.00 years, he also plans on being able to afford a 15-year mortgage with $1,594.00 monthly payments at a 5.40% APR interest rate. Given the graduate’s plans, how expensive of a lake house will he expect to be able to purchase? (assume that the house price will be the value of the savings and the loan)

Answer 1

Calculation of Value of savings in 10 years:

Nper = 10 * 4 = 40
Rate = 6.48% / 4
PMT = $1135
PV = 0

Value of savings in 10 years can be calculated by using the following excel formula:
=FV(rate,nper,pmt,pv)
=FV(6.48%/4,40,-1135,0)
= $63,182.52

Value of savings in 10 years = $63,182.52

Calculation of Value of loan:

Nper = 15 * 12 = 180
Rate = 5.40% / 12
PMT = $1594
FV = 0

Value of loan can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5.40%/12,180,-1594,0)
= $196,357.02

Price of the house = Value of savings + Value of loan
= $63,182.52 + $196,357.02
= $259,539.54

Price of the house = $259,539.54