Question

Some banks allow you to skip a loan payment and roll it into your principal. This is especially attractive in January when the Christmas VISA bill arrives. Consider the following simplified example. You renovated your house last year and borrowed $80,000. The term of the loan is three years, the rate is 8% (APR), and the annual (end-of-year) payments are $31,042.68. A year has passed and the first payment is due but you don’t have enough cash. Your bank has offered to add the first payment to the outstanding principal. What will your new (second and third) loan payments be? (Assume that the interest rate is still 8%.)

A) $40,000.00

B) $43,200.00

C) $44,319.21

D) $46,542.93

E) *$48,450.46

Looking for the process work to understand why the solution is E) $48,450.46.

Answer 1

Loan after 1 year=Loan*(1+rate)=80000*1.08=86400

Annual payments=Loan*rate/(1-1/(1+rate)^t)=86400*8%/(1-1/1.08^2)
=48450.4615385