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, INTEREST• Money that you earn or pay for the use of money.
• Always a percentage of the money deposited or borrowed.
• Different types of interest – depends on the way interest is calculated.
CHAPTER 2
• Simple Interest
• Simple Discount
SIMPLE INTEREST
• Interest is only calculated once during the time of the loan.
• It is a percentage of the present/principal value P. Thus interest is calculated as
I = Prt
I = Interest received/paid - money
P = Principal/present value
r = Interest rate per year
t = Time in years - if not change it to a fraction of a year. Thus divide by the number of
periods in one year
• The accumulated (future) amount S paid or received in future is calculated as the interest plus
the principal received/paid.
S=P+I
S = P + Prt
S = P(1 + rt)
ID words: Simple interest or simple interest rate
Calculator: Use normal mode, no financial keys exist.
SIMPLE DISCOUNT
• Interest is calculated only once.
• It is a percentage of the future value S. Thus discount (or interest) in this case called D, is
calculated as
D = Sdt
, D = Discount received/paid - money
S = Future value
d = Discount rate per year
t = Time in years - if not change it to a fraction of a year -> ÷ number of periods
in one year
• The present value received now is the future value S minus the discount D.
P=S–D
P = S – Sdt
P = S(1 – dt)
ID words: Simple discount or simple discount rate
Calculator: Use normal mode, no financial keys exist.
EQUATION OF VALUE
Sometimes we want to reschedule the payments of our debts that we owe someone. Instead of
paying back the loans as they were scheduled, we want to change the payments to other dates.
To calculate the sizes of the new payment or payments on the new payment dates we make use
of the equation of value concept that states that
the sum of all the obligations(loans or debts) = the sum of all the payments.
Now very important is that we can only compare or add moneys that are at the same time
period. This is because of the concept of time value of money. Namely that an amount of
money’s value changes over time. A loan increases over time or decreases if moved back in time,
due to interest added to a loan.
Thus, if we want to determine the sum of all the debts or payments at a specific date we need to
move all the moneys to the same date also called the comparison date before we can add or
subtract them.
Now if we move money forward in time we are calculating a future value (S) of that amount.
But the future value is calculated by using the formula S = P(1 + rt) in simple interest cases.
Thus we multiply the amount of money by an interest component (1 + rt).
Now if we move money back in time we are calculating a present value (P) of that amount. But
the present value is calculated by using the formula P = S/ (1 + rt) or written as P = S / (1 + rt)–1
in the simple interest cases. Thus we divide the amount of money by an interest component
(1 + rt) or multiply the amount by the interest component to the power of –1 .
, Now very important is to draw a time line of the problem as it helps you to determine the
time period t.
A lot of you have a problem with the time period t. The time period t is the period from where
you are moving the money from, to where you move the money to!!!!
The date that we move all the moneys to or the date at which the size of the payment is asked at
is called the comparison date.
Please work through the notes on equation of value on myUnisa under Announcements.
The notes are for compound interest but the same principles are used for simple interest.
Just use simple interest formula S = P (1 + rt) instead of compound interest.
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