Question

You want to take out a $324,000 mortgage (home loan). The interest rate on the loan is 5.3%, and the loan is for 30 years. Your monthly payments are $1,799.19.

1. How much will still be owed after making payments for 10 years? $__________Round your answers to the nearest dollar.
2. How much will still be owed after making payments for 15 years? $__________ Round your answers to the nearest dollar.
3. How much will still be owed after making payments for 20 years? $__________ Round your answers to the nearest dollar.

Answer 1

Monthly Payment = $1,799.19

Annual Interest Rate = 5.30%
Monthly Interest Rate = 5.30% / 12
Monthly Interest Rate = 0.441667%

Answer a.

Time Period = 20 years or 240 months

Loan Outstanding = $1,799.19/1.00441667 + $1,799.19/1.00441667^2 + … + $1,799.19/1.00441667^239 + $1,799.19/1.00441667^240
Loan Outstanding = $1,799.19 * (1 - (1/1.00441667)^240) / 0.00441667
Loan Outstanding = $1,799.19 * 147.788924
Loan Outstanding = $265,900

Answer b.

Time Period = 15 years or 180 months

Loan Outstanding = $1,799.19/1.00441667 + $1,799.19/1.00441667^2 + … + $1,799.19/1.00441667^179 + $1,799.19/1.00441667^180
Loan Outstanding = $1,799.19 * (1 - (1/1.00441667)^180) / 0.00441667
Loan Outstanding = $1,799.19 * 123.991121
Loan Outstanding = $223,084

Answer c.

Time Period = 10 years or 120 months

Loan Outstanding = $1,799.19/1.00441667 + $1,799.19/1.00441667^2 + … + $1,799.19/1.00441667^119 + $1,799.19/1.00441667^120
Loan Outstanding = $1,799.19 * (1 - (1/1.00441667)^120) / 0.00441667
Loan Outstanding = $1,799.19 * 92.990414
Loan Outstanding = $167,307