Page 122 - Maths Skills - 8

120 Maths

(ii) Calculation of Compound Interest When Interest is Compounded Half-Yearly
R
In such cases, if the rate = R% annually, then the rate for half-year = %.
2

Thus, the interest on half-year plus the original principal becomes the new principal for next half-year and so on.

(iii) Calculation of Compound Interest When Interest is Compounded Quarterly

In such cases, if the rate = R% per annum, then the rate Fact-o-meter
R
per quarter = %. Principal ×Rate× Time
4 Simple Interest=
Thus, the interest on the first quarter plus the original 100
principal becomes the new principal for the second
quarter and so on.

Let’s Attempt

Example 1: Find the Principal and the Amount if the simple interest for 3 years at the rate of 15% per annum
is ` 675.
Solution: Given: S.I. = ` 675 R = 15% per annum T = 3 years P = ?

P× R× T
S.I. =
100
100 100

∴ P = × S.I. = × 675 = ` 1500.
R× T 15× 3
Amount = Principal + Simple Interest = ` 1500 + ` 675 = ` 2175

Example 2: Find the compound interest on ` 2000 for 2 years at 10% per annum compounded annually.
Solution: Principal for the first year = ` 2000.
2000 10 1
S.I. for the first year = ` = ` 200
100
Amount at the end of first year = ` (2000 + 200) = ` 2200
∴ Principal for the second year = ` 2200
2200 10 1
S.I. for the second year = ` = ` 220
100
Amount at the end of second year = ` (2200 + 220) = ` 2420
∴ Compound interest = ` (2420 – 2000) = ` 420.
1
Example 3: Calculate the compound interest on ` 4000 for 1 years at 14% per annum compounded half-
2
yearly.
Solution: Given: Rate of interest = 14% annually

∴ Rate of interest for the half-year = 7% [As, compounded half-yearly]
1
Time = 1 years = 3 half-years
2
Original principal = ` 4000