Question

1. Sarah is planning to purchase her own home as her first real estate investment. The home is selling for $200,000 and she needs a 20% down payment. The loan will be for 30 years at 3.5% interest. What is Sarah’s monthly payment?

How much money would Sarah save over the life of the loan if she obtained a 15-year loan at the same rate?

If Sarah did not have the down payment and could save $850 per month at 2% APR compounded monthly, how long would Sarah have to save before she had the required down payment?

Answer 1

a)
PV = 200,000 * (1 - 20%) = 160,000
Nper = 30 * 12 = 360
Rate = 3.5% / 12
FV = 0

Monthly payment can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(3.5%/12,360,-160000,0)
= $718.47

Monthly payment = $718.47

b)
Total loan payment = $718.47 * 360 = $258,649.74

Monthly payment for 15 yaer loan can be calculated by using the following excel formula:
=PMT(rate,nper,pv,fv)
=PMT(3.5%/12,180,-160000,0)
= $1,143.81

Total payment for 15 year loan = $1,143.81 * 180 = $205,886.17

Amount of money Sarah would save over the life of the loan = $258,649.74 - $205,886.17 = $52,763.57

c)
Down payment = $200,000 * 20% = $40,000

PMT = 850
Rate = 2% / 12
FV = 40000
PV = 0

Number of years can be calculated by using the following excel formula:
=NPER(rate,pmt,pv,fv)
=NPER(2%/12,850,0,-40000)/12
= 3.78 Years