Page 198 - Start Up Mathematics_8 (Non CCE)

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 2: 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

,
¥¥
Ê 10 000 51ˆ
Interest for the first half year = ` Á Ë 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

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 3: 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
190