X 142 85712 114961 a 36 i 138 845031 i 36 x 142 7 112

X + 142 857.12 = 1149.61 a
36 i
+ 138 845.03(1 + i )
− 36
X + 142 857.12 = 37 286.97 + 112 950.52
X = $7380.37
Thus the penalty at the end of 2 years is $7380.37. If the penalty had been three
times the monthly interest on the outstanding balance at the end of 2 years, it
would have been
3 × 142 857.12 × .007363123 = $3155.62
■
EXAMPLE 4
The Wongs borrow $10 000 from a bank to buy some home
furnishings. Interest is j
12
= 9% and the term of the loan is 3 years. After
making 15 monthly payments, the Wongs miss the next two monthly payments.
The bank forces them to renegotiate the loan at a new, higher interest rate
j
12
= 10
1
2
%. Determine
a) the original monthly payments R
1
;
b) the outstanding balance of the loan at the time the 17th monthly payment
would normally have been made.
c) the new monthly payments R
2
if the original length of the loan term is not
extended.
Solution a
Using A = 10 000, n = 36, i =
.09
12
= .0075 we calculate the
original monthly payment
R
1
=
10 000
a
36 i
= $318.00
Solution b
The first 15 monthly payments of $318 were made. Therefore at
the end of 15 months the outstanding balance was
10 000(1 + i )
15
− 318 s
15 i
= 11 186.03 − 5028.75 = $6157.28
Then no payments were made for 2 months. Therefore the outstanding balance
at the end of 17 months is
$6157.28(1 + i )
2
= $6249.99
Solution c
We have A = 6249.99, n = 19, i =
.105
12
= .00875 and we calculate
the new monthly payment
R
2
=
6249.99
a
19 i
= $358.49
■
CHAPTER 5 • AMORTIZATION METHOD AND SINKING FUNDS
153

Part A
1.
A borrower is repaying a $5000 loan at
j
12
= 15%
with monthly payments
over 3 years. Just after the 12th payment (at the end of 1 year) he has the
balance refinanced at
j
12
= 12%
. If the number of payments remains
unchanged, what will be the new monthly payment and what will be the
monthly savings in interest?
2. A 5-year, $6000 loan is being amortized with monthly payments at j
12
= 18%.
Just after making the 30th payment, the borrower has the balance refinanced
at j
12
= 12% with the term of the loan to remain unchanged. What will be the
monthly savings in interest?
3. A borrower has a $5000 loan with the “Easy-Credit” Finance Company. The
loan is to be repaid over 4 years at j
12
= 24%. The contract stipulates an early
repayment penalty equal to 3 months’ payments. Just after the 20th payment,
the borrower determines that his local bank would lend him money at
j
12
= 16%. Should he refinance?
4. The Jones family buys a fridge and stove totalling $1400 from their local
appliance store. They agree to pay off the total amount with monthly
payments over 3 years at j
12
= 15%. If they wish to pay off the contract early
they will experience a penalty equal to 3 months’ interest on the effective
outstanding balance. After 12 payments they see that interest rates at their
local bank are j
12
= 11%. Should they refinance?
5. Consider a couple who bought a house in Canada in 1976. Assume they need-
ed a $60 000 mortgage, which was to be repaid with monthly payments over
25 years. In 1976, interest rates were j
2
= 10
1
2
%. What was their monthly
payment? In 1981 (on the 5th anniversary of their mortgage) their mortgage
was renegotiated to reflect current market rates. The repayment schedule was
to cover the remaining 20 years and interest rates were now j
2
= 22%. What
was the new monthly payment? What effect might this have on homeowners?