Page 123 - Maths Skills - 8

Comparing Quantities 121

4000 17
Interest for the first half-year = ` = ` 280.
100
Amount at the end of first half-year = ` (4000 + 280) = ` 4280

∴ Principal for the second half-year = ` 4280
4280 17
Interest for the second half-year = ` = ` 299.60.

100
Amount at the end of second half-year = ` (4280 + 299.60) = ` 4579.60
∴ Principal for the third half-year = ` 4579.60
 4579 60 17×× 
.
Interest for the third half-year = `   100  = ` 320.572

Amount at the end of third half-year = ` (4579.60 + 320.572) = ` 4900.172
Total compound interest = ` (4900.172 – 4000) = ` 900.172

Example 4: Find the compound interest on ` 4000 for half-year at 20% per annum compounded quarterly.
Solution: Given: Rate = 20% per annum

20
Quarterly rate = 4
% = 5%

Original principal = ` 4000
Time = Half-year = 2 quarters

400015
Interest for the first quarter = ` = ` 200.

100
Amount at the end of the first quarter = ` (4000 + 200) = ` 4200
∴ Principal for the second quarter = ` 4200

420015
Interest for the second quarter = ` = ` 210.

100
Amount at the end of the second quarter = ` (4200 + 210) = ` 4410
Amount at the end of the half-year = ` 4410

Hence, compound interest = ` (4410 – 4000) = ` 410.

Exercise 8.4

1. Find the compound interest on ` 15000 for 1 year at 16% per annum compounded half-yearly.

2. Find the compound interest on ` 16000, at 20% per annum for 1 year when compounded quarterly.
3. Rahul obtained a loan of ` 40000 for the purchase of a bike from a bank. If the rate of interest is 15%
per annum, then find the compound interest that he will have to pay after 2 years.
4. Find the compound interest on ` 10000 for 2 years at 10% per annum.