Question

You are buying a home and have saved $45,000 for a down payment. The house costs $360,000. You are given a choice by the mortgage banker. You can use your entire $45,000 for the down payment, and borrow $315,000 at a 4.2% annual rate with monthly payments of about $1540 per month for 30 years (360 monthly payments). Or you can buy down the interest rate by paying an upfront fee to the lender of $8,000. This will reduce the annual rate to 3.8%, but the loan amount will increase to $323,000 since you will have a smaller down payment.

Compute the exact monthly payment for the 4.2% 30-year loan with a starting balance of $315,000.

Compute the monthly payment for the mortgage with the lower interest rate and smaller down payment, so a 30-year mortgage at 3.8% with a starting balance of $323,000.

Compute the total interest paid over the loan of both loans.

Answer 1

Compute the exact monthly payment for the 4.2% 30-year loan with a starting balance of $315,000.
=315000*(4.2%/12)/(1-1/(1+4.2%/12)^(12*30))
=1540.40409720

Compute the monthly payment for the mortgage with the lower interest rate and smaller down payment, so a 30-year mortgage at 3.8% with a starting balance of $323,000.
=323000*(3.8%/12)/(1-1/(1+3.8%/12)^(12*30))
=1505.04224371

Compute the total interest paid over the loan of both loans.
Loan 1=1540.40409720*12*30-315000=239545.47499200
Loan 2=1505.04224371*12*30-323000=218815.20773560