Page 124 - Maths Skills - 8

122 Maths

5. Find the amount and the compound interest on ` 16000 for 3 years at 15% per annum.

6. Find out the compound interest on ` 15000 at 12% per annum for 6 months when compounded quarterly.
7. Vikas borrowed ` 25000 from his friend at 20% per annum compounded half-yearly. Find the amount of
1
money, which will discharge his debt after 1 years.
2

CALCULATION OF COMPOUND INTEREST BY USING FORMULAE
Formulae are used for calculation of compound interest.

Rule 1: When interest is compounded annually
Let Principal = ` P, Rate = R% per annum and Time = n years.


Then, the amount (A), after n years is given by the formula, A= P 1+ R  n


Compound Interest = Amount – Principal.  100
R n
C.I. = P 1 1
100

Rule 2: When interest is compounded annually, but the rates are different for different years
Let Principal = ` P, Time = 2 years, and Interest be R % and R % for the first year and second
1
2
year respectively.
Then, the Amount (A) after 2 years is given by A = P 1 R 1 1 R 2

100 100

Rule 3: When the interest is compounded annually, but the time is a fraction
x x
Let Principal = ` P, Rate = R% annually, and Time = n years, where n is a complete year and is
y
y
a fraction.
x
Then, the amount (A) after n years is given by A = P
y
4
For example; let the Time = 2 years
5
x 4 x 4
Now, n = 2 , so n = 2 years and = years.
y 5 y 5

Let’s Attempt

Example 1: What will be the amount on ` 20000 after 2 years, when the interest is compounded annually at
the rate of 10% per annum. Also calculate the compound interest.
Solution: Given: P = ` 20000 R = 10% per annum n = 2 years A = ?

n

Amount after 2 years P 1 R

100
10 2 110 110
= ` 20000 1 = ` 20000 = ` 24200
100 100 100
∴ Compound interest = ` (24200 – 20000) = ` 4200.