Page 197 - Start Up Mathematics_8 (Non CCE)

13 Compound Interest

Interest is a fee we pay for the use of borrowed money. It is the compensation paid by the borrower to the
lender as a percentage of the borrowed amount. The borrowed amount is called the principal and the percentage
of the principal paid over a certain period of time is called interest. There are two types of interest—simple
interest and compound interest.
You already know that simple interest is calculated only on the principal amount using the given formula:
PR T¥ ¥
Simple Interest (S.I.) = where P Æ Principal, R% Æ Rate of interest per annum and T Æ Time in
years 100
Simple interest is not a preferred method of lending for financial institutions, instead they employ compound
interest. In this method, interest is calculated on the amount of the previous year.

Compound Interest

In this method, the rate of interest and the time interval for compounding are fixed. The interest is calculated
on the principal after the first time interval. Then it is compounded/added to the principal. This amount then
becomes the principal for the next time interval and so on. Compounding of interest allows a principal amount
to grow at a faster rate than simple interest.
In the compound interest method, the rate of interest and time interval are fixed but the principal varies. In other
words, if the borrower and the lender agree to a certain time interval (like a year or a half year or a quarter of
a year or monthly or daily, etc.) and the rate of interest is also fixed, then Amount (Principal + Interest) at the
end of the first time interval becomes the principal for the next time interval and so on. The total interest over
the complete time period, so calculated is called the compound interest (C.I.). To put it simply, the borrower
is charged interest on previous interest also.
Conversion Period: The fixed time interval at the end of which the interest is calculated and then added to
the principal before the beginning of the next time interval is called the conversion period.
So, if the term says “compounded half-yearly”, it means the interest is calculated and added to the principal
every six months and the conversion period is six months. Remember
Similarly, if the term says “compounded quarterly”, it means the If no conversion period is specified,
interest is calculated and added to the principal every three months it is taken to be one year, i.e.,
(quarter) and the conversion period is three months.
compounded annually.

Computation of Compound Interest When Interest is Compounded Annually
Example 1: Find the compound interest on ` 1,200 for two years at 5% per annum.

Solution: Principal for the first year = ` 1,200
¥
¥
Ê 1,200 5 1¥¥ ˆ Ê P R Tˆ
Interest for the first year = ` Á Ë 100 ˜ ¯ = ` 60 Á UsingS.I.= 100 ˜
Ë
¯
Amount at the end of first year = ` 1,200 + ` 60 = ` 1,260
¥
¥
Ê 1,260 5 1¥¥ ˆ Ê P R Tˆ
Interest for the second year = ` Á Ë 100 ˜ ¯ = ` 63 Á UsingS.I.= 100 ˜
¯
Ë