Joanne and Bill are financing $305,500 to purchase a house. They obtained a 20/6 balloon mortgage at 5.75%. What will their balloon payment be?
$206,311.68
$401,524.25
$152,285.77
$249,295.69
My answer is the 4th one.
To calculate the balloon payment for a mortgage, you need to know the loan amount, the interest rate, and the loan term. In this case, Joanne and Bill have a 20/6 balloon mortgage, which indicates a loan term of 20 years with a balloon payment due after 6 years.
To calculate the balloon payment, we first need to determine the monthly mortgage payments for the first 20 years. We can use the formula for calculating a mortgage payment:
M = P [ i(1+i)^n ] / [ (1+i)^n - 1 ]
Where:
M is the monthly mortgage payment,
P is the loan amount,
i is the monthly interest rate, and
n is the total number of monthly payments.
First, we need to calculate the monthly interest rate. The annual interest rate of 5.75% needs to be divided by 12 (the number of months in a year) to get the monthly interest rate. Hence, i = 5.75%/12 = 0.0047917.
Next, we need to calculate the total number of monthly payments for the first 20 years. Since there are 12 months in a year and the loan term is 20 years, n = 20 * 12 = 240.
Now, we can plug these values into the formula to calculate the monthly mortgage payment:
M = $305,500 [ 0.0047917(1+0.0047917)^240 ] / [ (1+0.0047917)^240 - 1 ]
M = $1,839.66 (rounded to the nearest cent)
Joanne and Bill will make monthly mortgage payments of approximately $1,839.66 for the first 20 years. However, after 6 years, they will need to make the balloon payment.
To calculate the balloon payment, we need to determine the remaining loan balance after the 20-year term. Since there are 6 years remaining, we can calculate the remaining loan balance using the formula:
B = P [ (1+i)^n - (1+i)^p ] / [ (1+i)^n - 1 ]
Where:
B is the remaining loan balance,
P is the loan amount,
i is the monthly interest rate,
n is the total number of monthly payments (20 years = 240), and
p is the number of payments already made (20 years = 240 minus 6 years = 180).
Plugging in the values:
B = $305,500 [ (1+0.0047917)^240 - (1+0.0047917)^180 ] / [ (1+0.0047917)^240 - 1 ]
B = $249,295.69 (rounded to the nearest cent)
Therefore, Joanne and Bill's balloon payment will be $249,295.69. So, your answer, the 4th option, is correct.