Page 126 - Maths Skills - 8

124 Maths

SOME ADDITIONAL CASES

Rule 1: When Interest is Compounded Half-Yearly
Let Principal = ` P, Rate = R% annually, and Time = n years.
R
When interest is compounded half-yearly, then rate = % and Time = (2n) half-years.
2
R/ 2 2n
Therefore, Amount (A) = P 1 and C.I. = A – P.

100

Rule 2: When Interest is Compounded Quarterly
Let Principal = ` P, Rate = R% per annum, and Time = n years.

R
When interest is compounded quarterly, then rate = % and time = 4n quarters.
4

Therefore, A= P 1 R/ 4 4n and C.I. = A – P.

100

Let’s Attempt

Example 1: Find the compound interest on ` 20000 for 2 years at 20% per annum when compounded half-
yearly.
Solution: Given: P = ` 20000 R = 20% per annum, compounded half-yearly
n = 2 years A = ?

R/ 2 2n 10 4 110 4
Amount (A) after 2 years = P 1 = ` 20000 1 = ` 20000

100 100 100
11 11 11 11
= ` 20000 = ` 29282

10 10 10 10
Compound interest = ` (29282 – 20000) = ` 9282.
Example 2: Find out the compound interest on ` 10000 for 6 months at 8% per annum compounded quarterly.

Solution: Given: P = ` 10000 R = 8%, compounded quarterly

6 1
n = 6 months = year = year A = ?
12 2
R/ 4 4n 8/ 4 4 1 2 2 2
Amount (A) after 6 months = P 1 = ` 10000 1 = ` 10000 1
100 100 100

102 2 102 02
= ` 10000 = ` 10000 = ` 10404

100 100 100
∴ Compound interest = ` (10404 – 10000) = ` 404.