Lecture 5
Loans and Costs of Borrowing
1

Loan
balance:
prospective
method
and
retrospective method
Amortization schedule
Sinking fund
Varying installments and varying interest rates
Quoted rate of interest and equivalent nominal
rate of interest in monthly rest
Flat rate loan and flat rate discount loan
Annual percentage rate, annual percentage
yield, effective rate of interest, and comparison
rate of interest
2

Consider a loan with a fixed term of maturity,
to be redeemed by a series of repayments.
If the repayments prior to maturity are only to
offset the interests, the loan is called an
interest-only loan.
If the repayments include both payment of
interest
and
partial
redemption
of
the
principal, the loan is called a repayment loan.
We consider two approaches to compute the
balance of the loan: the prospective method
and the retrospective method.
3

The
prospective
method
is
forward
looking. It calculates the loan balance as the
present value of all future payments to be
made.
The
retrospective method
is backward
looking. It calculates the loan balance as the
accumulated value of the loan at the time of
evaluation minus the accumulated value of
all installments paid up to the time of
evaluation.
4

Example:
A housing loan of $400,000 was to
be
repaid
over
20
years
by
monthly
installments of an Ordinary annuity at the
nominal rate of 5% per year. After the 24th
payment was made, the bank increased the
interest rate to 5.5%.
If the lender was required to repay the loan
within the same period, how much would be
the increase in the monthly installment.
If the installment remained unchanged, how
much longer would it take to pay back the
loan?
5

Ordinary Annuity
Part (a)
Initial payment was:
C=?; where PVA = 400 000; k=0.05/12:
n=20*12=240
C=$2639.82
Amount that needs to be paid after the
increase in rates: PVA=? Where k=0.05/12;
n=240-24=216
PVA=$375 489.74
6

Payment amount after the increase in
interest C=?; where PVA = 375 489.74;
k=0.055/12: n=216
C=$2742.26
so that the increase in installment is
$2742.26-$2639.82
= 102.44
7

Part (b)
If the installment remained unchanged, you
have to calculate n, where PVA =375489.74;
c=$2639.82: k=0.055/12 using:
You will get n=231
So additional months is:
231-216 =
15 months
8

Example :

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- Spring '15
- Annual Percentage Rate, Debt, Interest, Interest Rate, Mortgage loan