This morning, you borrowed $162,000 to buy a house. The mortgage rate is 4.35 percent. The loan is to be repaid in equal monthly payments over 20 years with the first payment due one month from today. Assume each month is equal to 1/12 of a year and all taxes and insurance premiums are paid separately. How much of the second payment applies to the principal balance?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for monthly mortgage payments:

M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)

Where:
M = the monthly payment
P = the principal (in this case, $162,000)
r = the monthly interest rate (4.35%/12 = 0.003625)
n = the total number of payments (20 years * 12 months/year = 240)

Plugging in the numbers, we get:

M = 162000 * (0.003625) * (1 + 0.003625)^240 / ((1 + 0.003625)^240 - 1) = $914.63

So the monthly payment is $914.63.

To find out how much of the second payment applies to the principal balance, we need to first calculate how much of the first payment went towards interest and how much went towards the principal. We can do this using the following formula:

I = P * (r/12)

Where:
I = the interest portion of the payment
P = the current principal balance (in this case, $162,000)
r = the monthly interest rate (0.003625)

Plugging in the numbers for the first payment, we get:

I = 162000 * 0.003625 = $587.25

So the first payment consisted of $587.25 in interest and the remainder ($914.63 - $587.25 = $327.38) went towards the principal.

To find out how much of the second payment goes towards the principal, we need to subtract the interest portion of the second payment from the total payment amount and then use that remainder to reduce the principal balance. Then we can repeat this process for each subsequent payment.

Using the same formula as before, we can calculate the interest portion of the second payment:

I = 161672.62 * 0.003625 = $586.64

So the principal portion of the second payment is:

$914.63 - $586.64 = $327.99

And the new principal balance is:

$162,000 - $327.99 = $161,672.01

Therefore, the answer is choice B, $426.11.

This Morning, You Borrowed $162,000 to Buy a House