Shantle and Kwamie are planning to buy their first home. Although they are excited about the prospect of being homeowners, they are also a little frightened. A mortgage payment for the next 30 years sounds like a huge commitment. They visited a few developments and scanned the real estate listings of per owned homes, but they really have no idea how much a mortgage payment would be on a $150,000, $175,000, or $200,000 loan. They have come to you advice.

Question

After you explain to then that they can borrow money at different amounts of time, Shantel and Kwamie ask you to complete a chart indicating what the monthly mortgage payment would be under some possible interest rates and borrowing periods. They also went to know what their total interest would be on each if they chose a 25-year loan. Complete the chart.
Amount 6.25% 6.5% 6.75% 7% total interest
borrowed 15 yrs 20 yrs 25 yrs 30 yrs Paid
$150,000
$175,000
$200,000

2. If Shantel and Kwamie made a down payment of $200,000 or a $175,000 home, what would be their monthly mortgage payment assuming they finance for 25 years at 6.75%? How much would they save on each monthly payment by making the down payment? How much interest would they save over the life of the loan?

Answer 1

First, let's complete the chart with the monthly mortgage payments using the formula:
M = P × r × (1+r)^n / ((1+r)^n - 1)
Where:
M = Monthly payment
P = Loan amount
r = Monthly interest rate (annual interest rate/12)
n = Total number of payments (loan period*12)

For example, for $150,000 borrowed, 15 years loan period, and 6.25% interest rate:
M = 150,000 × (0.0625/12) × (1+0.0625/12)^(15*12) / ((1+0.0625/12)^(15*12) - 1)

To calculate the total interest paid, find the total amount paid over the loan period and subtract the original loan amount.
Total Interest = (Monthly Payment * Loan Period * 12) - Original Loan Amount

I will list out the values of monthly mortgage payments and total interest paid for each loan amount, interest rates, and loan periods.

$150,000 borrowed:
6.25%: 15 yrs - $1,230.51, 20 yrs - $982.04, 25 yrs - $867.68, 30 yrs - $798.36
Total Interest: $150,000 × 25 yrs × 6.75% = $266,092 - $150,000 = $116,092

$175,000 borrowed:
6.25%: 15 yrs - $1,435.45, 20 yrs - $1,145.74, 25 yrs - $1,012.30, 30 yrs - $931.41
Total Interest: $175,000 × 25 yrs × 6.75% = $310,441 - $175,000 = $135,441

$200,000 borrowed:
6.25%: 15 yrs - $1,640.49, 20 yrs - $1,309.39, 25 yrs - $1,156.97, 30 yrs - $1,064.48
Total Interest: $200,000 × 25 yrs × 6.75% = $354,791 - $200,000 = $154,791

Now, let's answer the second question. If they made a down payment of $200,000 on a $175,000 home, they would actually be paying $25,000 less than the asking price. They would only need a loan for $150,000.

Using the formula, their monthly mortgage payment for a 25-year loan at a 6.75% interest rate would be $1,029.29.

Comparing to the original monthly payment for the $175,000 home at 6.75% for 25-years($1,156.97), they would save $1,156.97 - $1,029.29 = $127.68 for each monthly payment.

To find out how much interest they would save over the life of the loan, compare the total interest paid on both the $150,000 loan and the $175,000 loan.
Total interest paid difference = $135,441 - $116,092 = $19,349

Therefore, Shantel and Kwamie would save $19,349 in interest over the life of the loan by making the down payment.