Page 125 - ICSE Math 8

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 Maths Info
period is six months. If no conversion period is
Similarly, if the term says “compounded quarterly”, it means the specified, it is taken to be one
interest is calculated and added to the principal every three months year, i.e., compounded annually.
(quarter) and the conversion period is three months.

Computation of compound interest when interest is compounded annually
Example 7: Find the compound interest on ` 1,200 for two years at 5% per annum.
Solution: Principal for the first year = ` 1,200
 1,200 5 1× ×   P R× × T 
Interest for the first year = `   = ` 60  Using=I 
 100   100 
Amount at the end of first year = ` 1,200 + ` 60 = ` 1,260
 1,260 5 1× ×   P R× × T 
Interest for the second year = `   = ` 63  Using=I 
 100   100 
Amount at the end of second year = ` 1,260 + ` 63 = ` 1,323
\ Compound interest = ` (1,323 – 1,200) = ` 123

Compound Interest can also be calculated by adding the interest for each year.

Computation of compound interest when interest is compounded half-Yearly
r
If the rate of interest is r% per annum, then, on compounding half-yearly, the rate of interest will become %
2
per half year. Also, the time is then converted in terms of half year. For example, if the time is n years, then,
we write it as 2 × n half years.
1
Example 8: Find the compound interest on ` 10,000 for 1 years at 10% per annum, interest being payable
half-yearly. 2
1
Solution: Rate of interest = 10% per annum = 5% per half year, Time = 1 years = 3 half years
2
Original principal = ` 10,000
××
,
 10 000 51
Interest for the first half year = `   100   = ` 500
\ Amount at the end of the first half year = ` (10,000 + 500) = ` 10,500
Principal for the second half year = ` 10,500
¥¥
,
Ê 10 500 51ˆ
Interest for the second half year = ` Á Ë 100 ˜ = ` 525
¯
\ Amount at the end of the second half year = ` (10,500 + 525) = ` 11,025
Principal for the third half year = ` 11,025
,
¥¥
Ê 11 025 51ˆ
Interest for the third half year = ` Á Ë 100 ˜ = ` 551.25
¯
\ Amount at the end of the third half year = ` 11,025 + ` 551.25 = ` 11,576.25
\ Compound interest = ` 11,576.25 – 10,000 = ` 1,576.25

113