Question

This morning, you took out a loan of $386,000 to purchase a home. The interest rate on the 30-year mortgage is 3.75 percent and you will make monthly payment. You have decided to make additional monthly payment of $360 beginning with the first payment that will occur one month from today. By how many years will you shorten the length of time it will take you to pay off the loan?

Group of answer choices

11.06 years

9.33 years

12.84 years

7.97 years

Answer 1

Loan amount = $386,000

Monthly Interest rate = 3.75%/12 = 0.3125%

No of payments = 30*12 = 360

Calculating the Monthly Paymnet of Loan using Excel"PMT" function:-

Monthly Payment = $1787.63

- You have decided to make additional monthly payment of $360 beginning with the first payment that will occur one month from today

New Monthly paymnet of Loan = $1787.63 + $360

= $2147.63

Now, calculating the number of months it will take to pay off the loan using Excel "NPER" function:-

Number of Months loan will be paid off = 264.34

Number of Years the loan period will be shortened = (360months - 264.34months)/12 months

Number of Years the loan period will be shortened = 7.97

Option D

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