Question

Chandler and Monica Bing wish to buy a new home. The listing price is $387,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 9% fixed APR for 30 years, with monthly payments to begin in one month. For simplicity, let’s ignore closing costs and taxes when solving this question.

c 1). Suppose they chose the 30-year plan and 20 years have passed since the loan started. They have made the past 240 payments exactly on time. What is the remaining balance on their loan now?

c 2). Chandler and Monica’s rich actor friend Joey decides to help them pay a lump sum $100,000 on their remaining balance. After the help from this generous friend, what is their remaining balance at year 20?

c 3). If Chandler and Monica decide to make equal monthly payment for the 10 years left for the remaining balance after this generous help from Joey, what will their monthly payment be?

Answer 1

Finding the monthly payment

Loan= Monthly payments*(1-1/(1+rate)^number of terms)/rate

387500*80%= Monthly payment*(1-1/(1+9%/12)^360)/(9%/12)

310000= P*124.2818657

P= 310000/124.2818657

=2,494.33

c1) Balance payments on the loan= 360-240=120

Loan balance= Monthly payments*(1-1/(1+rate)^number of terms)/rate

= 2494.33*(1-1/(1+9%/12)^120)/(9%/12)

=2494.33*78.94169267

=196906.63

c2) Remaining balance=196906.6323-100000

=$ 96906.63

c3) Loan balance= Monthly payments*(1-1/(1+rate)^number of terms)/rate

96906.63= P*(1-1/(1+9%/12)^120)/(9%/12)

96906.63= P*78.94169267

P= $1227.57