Page 126 - ICSE Math 8

Computation of compound interest when interest is compounded quarterly
r
If the rate of interest is r% per annum, then, on compounding quarterly, rate of interest will become % per
4
quarter. Also, the time will be calculated in terms of quarters. For example, if the time is n years, then, we
write it as 4 × n quarter years.

Example 9: Find the compound interest on ` 6,000 for 1 year at the rate of 16% per annum compounded
quarterly.
16
Solution: Rate of interest = 16% per annum = % = 4% per quarter, Time = 1 year = 4 quarters
4
Principal for the first quarter = ` 6,000, Rate of interest = 4%
,
¥¥
Ê 6 000 41ˆ
Interest for the first quarter = ` Á 100 ˜ = ` 240
¯
Ë
\ Amount at the end of the first quarter = ` (6,000 + 240) = ` 6,240
Principal for the second quarter = ` 6,240, Rate of interest = 4%
¥¥
,
Ê 6 240 41ˆ
Interest for the second quarter = ` Á Ë 100 ˜ = ` 249.60
¯
\ Amount at the end of the second quarter = ` (6,240 + 249.60) = ` 6,489.60
Principal for the third quarter = ` 6,489.60, Rate of interest = 4%
,
¥¥
.
Ê 6 489 60 41ˆ
Interest for the third quarter = ` Á 100 ˜ = ` 259.584
Ë
¯
\ Amount at the end of the third quarter = ` (6,489.60 + 259.584) = ` 6,749.184
Principal for the fourth quarter = ` 6,749.184, Rate of interest = 4%
.
,
¥¥
Ê 6 749 184 41ˆ
Interest for the fourth quarter = ` Á Ë 100 ˜ = ` 269.97
¯
\ Amount at the end of the fourth quarter = ` (6,749.18 + 269.97) = ` 7,019.15
\ Compound interest = ` (7,019.15 – 6,000) = ` 1,019.15
EXERCISE 11.2

1. Rahul invested ` 7,000 in shares for 2 years at the rate of 12% per annum compounded annually. What
is the compound interest that Rahul gets after 2 years?
1
2. Find the compound interest on ` 3,000 at the rate of 6% per annum for 1 years compounded half-yearly.
2 1
3. Veena borrowed ` 20,000 from a money lender at the rate of 4% per annum for 1 years compounded
1 2
half-yearly. Find the amount she has to pay at the end of 1 years.
2
4. Find the compound interest on a sum of ` 12,000 at the rate of 8% per annum for 1 year compounded
quarterly.
5. Ruchi borrowed ` 18,000 from her friend at the rate of 12% per annum at simple interest. She lent it
further to another friend Aarti at the same rate but compounded annually. Find the profit that Ruchi earns
after 2 years.
6. Kavya deposited ` 8,500 in a bank which pays her 12% interest per annum compounded quarterly. What
is the amount which she receives after 9 months?

Computation of Compound Interest Using Formulae
The formula for simple interest is used in deriving the formula for compound interest. Let us derive formulae
for compound interest when interest in compounded annually, half yearly and quarterly.

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