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.

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?

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.

To calculate the monthly mortgage payment for different loan amounts, interest rates, and borrowing periods, we can use the formula for calculating the monthly payment on a fixed-rate mortgage:

Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

1. Let's complete the chart for different loan amounts and borrowing periods:

Amount borrowed: $150,000
- 15 years at 6.25%
- 20 years at 6.5%
- 25 years at 6.75%
- 30 years at 7%
- Total interest paid over 25 years

Amount borrowed: $175,000
- 15 years at 6.25%
- 20 years at 6.5%
- 25 years at 6.75%
- 30 years at 7%
- Total interest paid over 25 years

Amount borrowed: $200,000
- 15 years at 6.25%
- 20 years at 6.5%
- 25 years at 6.75%
- 30 years at 7%
- Total interest paid over 25 years

2. To calculate the monthly mortgage payment for a $175,000 home with a 25-year loan term and an interest rate of 6.75%:

Loan amount: $175,000
Loan term: 25 years
Interest rate: 6.75%

Using the formula mentioned earlier, we can calculate the monthly payment:

Monthly Interest Rate = (Annual Interest Rate / Number of Months in a Year) = (6.75% / 12)
Number of Months = Loan Term * 12 = 25 * 12

Monthly Payment = ($175,000 * (6.75% / 12)) / (1 - (1 + (6.75% / 12))^(-25 * 12))

To calculate the savings on each monthly payment when making a down payment, subtract the monthly payment with the down payment from the monthly payment without the down payment.

Interest Savings over the life of the loan can be calculated by subtracting the total interest paid with the down payment from the total interest paid without the down payment.

Please note that I am unable to provide the exact values of the monthly payment, savings, and total interest without a specific interest rate for each loan term in the chart.

To calculate the monthly mortgage payment and total interest for different loan amounts, interest rates, and borrowing periods, you can use a mortgage calculator or formula. However, for this explanation, let's focus on the formula:

Monthly Mortgage Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:
P = Principal (loan amount)
r = Monthly interest rate (Annual interest rate divided by 12, and expressed as a decimal)
n = Total number of monthly installments (loan term in years multiplied by 12)

Now, let's fill in the chart for the given loan amounts and borrowing periods:

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

To calculate the monthly mortgage payment amount, plug in the values into the formula for each scenario.

For example, let's calculate the monthly mortgage payment for a $150,000 loan with a 6.25% interest rate and a borrowing period of 15 years:

P = $150,000
r = 6.25% / 12 = 0.0052 (monthly interest rate)
n = 15 years * 12 = 180 months

Using the formula:

Monthly Mortgage Payment = $150,000 * 0.0052 * (1 + 0.0052)^180 / ((1 + 0.0052)^180 - 1)

Calculate this for each scenario (amount borrowed, interest rate, and borrowing period), and you will have the monthly mortgage payment for each case.

Now, let's move on to the second part of the question:

If Shantel and Kwamie made a down payment of $200,000 on a $175,000 home, the loan amount would be $175,000 - $200,000 = $0 (they would not need to finance). Therefore, their monthly mortgage payment would be $0.

By making the down payment, they would save the full mortgage payment amount each month.

In terms of interest saved over the life of the loan, it would be the total interest paid on a $175,000 loan with a 25-year term at a 6.75% interest rate. To calculate the total interest, you can use the formula:

Total Interest = (Monthly Mortgage Payment * Total Number of Payments) - Loan Amount

Calculate this for the original scenario (before the down payment) and subtract it from the total interest paid on a $175,000 loan over 25 years to find the amount of interest saved.

Remember, it's always a good idea to use a mortgage calculator or consult with a financial advisor to get accurate and up-to-date information for your specific situation.