Question

1. A borrower has a 30-year mortgage loan for $200,000 with an interest rate of 6% and monthly payments. If she wants to pay off the loan after 8 years, what would be the outstanding balance on the loan? (D)
2. 1. $84,886
   2. $91,246
   3. $146,667
   4. $175,545
   5. Not enough information

Please explain me the step on financial calculator. The answer is D

Answer 1

At first, we have to compute the monthly payment amount for the loan. (PMT function)

n (number of monthly payments) = 30*12 = 360

1/Y (Interest rate) = 6/12 = 0.5

PV = $200,000 (Loan amount at present)

FV = 0

In the Financial calculator, follows the following steps:

N = 360

1/Y = 0.5

PV = 200,000

FV = 0

CPT (Compute) PMT.

This shall give us PMT = $ 1,199.10

Note: The value will come up as - $ 1,199.10 as the calculator assumes we will be paying this (withdrawal/ outflow)

Now, the question states that the borrower wishes to pay-off her entire amount of loan after 8 years. Thus, we must find the present value of the amount she would need to pay at end of the 8th year to completely pay off the loan.

After 8 years, the payments already over are 96 (8*12). Thus, the remaining number of payments are 264 (360-96)

n = 264

1/Y = 0.5

FV = 0

PMT = $ 1,199.10

In the Financial calculator, follows the following steps:

N = 264

1/Y = 0.5

PMT = 1,199.10

FV = 0

CPT (Compute) PV.

This shall give us PV = $ 175,545. (Option D)