# TVM Question (Prepayment)

A house of \$ 120,000 is purchased through a mortgage loan with the following characteristics: annual rate of 10% for 10 years with annual payments at the end of each year and amortizing from the 2nd year (the 1st is not amortized but it is pays interest). At the end of the 6th year it is decided to prepay the loan. What is the amount to prepay? (Choose the closest alternative)

a. 48 000
b. 61 500
c. 60 500

Okay this is what I did.

First I compute PMT considering 9 years because 1st year is not amortized:

N 9, I/Y 10, PV 120 000, PMT 20 836.86, then in the end of the 6th year the balance that will be prepaid is
N 4, I/Y 10, PMT 20 836.86, PV 66050 (the prepayment)

I considered N 10 as well, and I got PV 61 905.69 (the prepayment)

But there is no that answer.

Am I missing smth?

I’m coming up with the same answer as you:

PV -120000
INT 0.1
N 9
FV 0
YEAR BEG INT PMT PRIN END
1 120,000 12,000 12,000 - 120,000
2 120,000 12,000 20,837 8,837 111,163
3 111,163 11,116 20,837 9,721 101,443
4 101,443 10,144 20,837 10,693 90,750
5 90,750 9,075 20,837 11,762 78,988
6 78,988 7,899 20,837 12,938 66,050
7 66,050 6,605 20,837 14,232 51,818
8 51,818 5,182 20,837 15,655 36,163
9 36,163 3,616 20,837 17,221 18,943
10 18,943 1,894 20,837 18,943 (0)