A couple buys a $170000 home, making a down payment of 18%. The couple finances the purchase with a 15 year mortgage at an annual rate of 2.75%. Find the monthly payment.
To find the monthly mortgage payment, we first need to calculate the loan amount.
The down payment made by the couple is 18% of the home's purchase price. So, the amount financed is 100% - 18%, which is 82%.
The loan amount is calculated by multiplying the purchase price by the percentage financed:
Loan Amount = Purchase Price * Percentage Financed
Loan Amount = $170,000 * 82%
Loan Amount = $170,000 * 0.82
Loan Amount = $139,400
Next, we can calculate the monthly interest rate by dividing the annual rate by 12 (months).
Monthly Interest Rate = Annual Interest Rate / 12
Monthly Interest Rate = 2.75% / 12
Monthly Interest Rate = 0.02292
Now, we can calculate the monthly mortgage payment using the following formula:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ -number of months)
In this case, the loan term is 15 years, which is equal to 15 * 12 = 180 months.
Using the given values, we can now calculate the monthly payment:
Monthly Payment = ($139,400 * 0.02292) / (1 - (1 + 0.02292) ^ -180)
Monthly Payment= $319.05
Therefore, the monthly mortgage payment for the couple is $319.05.
To find the monthly payment on a mortgage, we can use the formula for calculating the monthly payment on a fixed-rate mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
Where:
M = monthly payment
P = principal amount (loan amount)
i = monthly interest rate
n = number of monthly payments
Let's break down the given information to solve the problem step by step:
1. Calculate the loan amount:
The couple made a down payment of 18% on a $170,000 home. Therefore, the loan amount can be calculated as:
Loan amount = $170,000 - (18% of $170,000)
Loan amount = $170,000 - ($170,000 * 0.18)
Loan amount = $170,000 - $30,600
Loan amount = $139,400
2. Calculate the monthly interest rate:
The annual interest rate is 2.75%. To convert it into a monthly interest rate, divide it by 12 months:
Monthly interest rate = 2.75% / 12
Monthly interest rate = 0.0229167
3. Calculate the total number of monthly payments:
The mortgage term is 15 years. Multiply it by 12 months to get the total number of monthly payments:
Total number of monthly payments = 15 years * 12 months
Total number of monthly payments = 180
4. Substitute the values into the monthly mortgage payment formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
M = $139,400 [ 0.0229167(1 + 0.0229167)^180 ] / [ (1 + 0.0229167)^180 - 1 ]
Now, use a calculator or spreadsheet software to evaluate this expression to get the monthly payment amount. The result will be the monthly payment the couple needs to make for their mortgage.