To calculate how much the buyer will save in interest with the 15-year mortgage option compared to the 30-year option, we need to follow these steps:

Step 1: Calculate the Down Payment

The bank requires a 15% down payment on a home priced at $120,000. $\text{Down Payment} = 15\% \times 120,000 = 0.15 \times 120,000 = 18,000$ So, the down payment is $18,000.

Step 2: Calculate the Loan Amount

The loan amount is the price of the home minus the down payment: $\text{Loan Amount} = 120,000 - 18,000 = 102,000$ Thus, the loan amount is $102,000.

Step 3: Mortgage Payments Calculation

Mortgage Formula:

The formula for calculating the monthly mortgage payment is given by: $M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1}$ Where:

• $M$ = monthly payment
• $P$ = loan amount (principal)
• $r$ = monthly interest rate (annual interest rate divided by 12)
• $n$ = total number of payments (loan term in years multiplied by 12)

We will calculate the monthly payment for both the 15-year and 30-year mortgage options.

15-Year Mortgage (at 10%)

• Annual Interest Rate = 10% → Monthly Interest Rate = $\frac{10\%}{12} = 0.00833$
• Loan Term = 15 years → Total Number of Payments $n = 15 \times 12 = 180$

Substituting the values into the formula: $M_{15} = 102,000 \times \frac{0.00833(1 + 0.00833)^{180}}{(1 + 0.00833)^{180} - 1}$

30-Year Mortgage (at 10%)

• Annual Interest Rate = 10% → Monthly Interest Rate = $\frac{10\%}{12} = 0.00833$
• Loan Term = 30 years → Total Number of Payments $n = 30 \times 12 = 360$

Substituting the values into the formula: $M_{30} = 102,000 \times \frac{0.00833(1 + 0.00833)^{360}}{(1 + 0.00833)^{360} - 1}$

Step 4: Calculate Total Interest Paid

For each mortgage option:

1. Multiply the monthly payment by the total number of payments to get the total amount paid.
2. Subtract the original loan amount from the total to get the total interest paid over the life of the loan.

Now, let's calculate the values.### Results:

• 15-Year Mortgage:

  • Monthly Payment: $1,096.10
  • Total Interest Paid: $95,297.50

• 30-Year Mortgage:

  • Monthly Payment: $895.12
  • Total Interest Paid: $220,244.28

Interest Savings:

By choosing the 15-year mortgage, the buyer would save $124,946.78 in interest compared to the 30-year option.

Would you like more details on these calculations, or do you have any further questions?

Here are 5 follow-up questions:

1. What factors could influence a buyer's decision to choose a 15-year over a 30-year mortgage, aside from interest savings?
2. How does the monthly payment compare to the buyer's budget for each option?
3. How do early payments or prepayment options affect total interest?
4. What impact would a lower interest rate have on both mortgage options?
5. How does a down payment impact the overall loan amount and interest calculations?

Tip: Always compare the total interest paid over the life of the loan to see the long-term financial impact, not just the monthly payments.