Carissa has a 30-year, 5.75% mortgage on her $250,000 home. She has been paying on it for 5 years, and has recently hit some financial trouble. If her
lender agreed to lower the interest rate on her $231,905.47 balance to 5.25%,
what will her new payment be for the remainder of the loan?
A. $1389.69
B. $1333.09
C. $1330.20
D. $1432.09

A. $1389.69

Step-by-step explanation:

To calculate the new monthly mortgage payment that Carissa will start paying going forward, we use the formula for calculating monthly mortgage payments.

The formula is:- M = P { [r ( 1+ r)^n] ÷ [ ( (1+r)^n) -1] }

Here, M is the monthly mortgage payment.

P is the principal

r is the monthly interest rate calculated by dividing your annual interest rate by 12

n is the number of payments(the number of months you will be paying the loan).

Hence, the new principal that Carissa must payback is $231,905.47¢.

The annual interest rate has been reduced to 5.25% from 5.75%.

Therefore, the new monthly interest rate will be obtained by dividing the new annual interest rate by 12

= 5.25%/2

= 0.438%

This is the new monthly interest rate.

Since she has been paying her mortgage loan diligently for 5 complete years. It means she now has just 25 years to complete the payment. If 12 months make up one year, then there are - 12 × 25 = 300 more months to go.

300 is, therefore "n" that is required for the calculation.

All the terms needed for the calculation of her new monthly mortgage are now complete.

P = $231,905.47¢

r = 0.4375%

n = 300

M = 231,905.47 { [0.004375 (1+0.004375) ^300] ÷ [ ( (1+0.004375) ^ 300 ) - 1] }

= 231,905.47 { [ 0.004375 (3.7048) ] ÷ (2.7048) }

= 231,905.47 × 0.005992

M = $1,389.69

Therefore her new monthly mortgage payment will become $1,389.69