Page 123 - ICSE Math 8

Example 2: Calculate the interest on ` 2,700 from 14 October 2013 to 21 May 2014 at the rate of 4 %
per annum.
Oct Nov Dec Jan Feb Mar Apr May Maths Info
Solution: T = 17 + 30 + 31 + 31 + 28 + 31 + 30 + 21 To find the time period, the day on
219 3
= 219 days = 365 year = year which money is borrowed is not taken
5
into account, but the day on which
2,700 × 4 × 3 money has to be returned is counted.
I = ` 100 × 5 = ` 64.80
1
Example 3: Sheena borrowed ` 7,000 from her friend for 2 years and 4 months at the rate of 1 % per
2
annum. Find the amount she has to return at the end of 2 years.
1 3
Solution: R = 1 % = %
2
2
7

T = 2 years 4 months = 2 + 4   years = 24 + 4 years = 28 years = years

12
3
12
 12 
P × R × T 7,000 × 3 × 7
I = 100 = ` 100 × 2 × 3 = ` 245
∴ Amount = P + I = ` (7,000 + 245) = ` 7,245
Example 4: A certain sum amounts to ` 3,825 in 4 years and to ` 4,050 in 6 years. Find the principal and
the rate of interest per annum.
Solution: Amount in 4 years = ` 3,825
i.e., Principal + Interest of 4 years = ` 3,825 ... (1)
Amount in 6 years = ` 4,050
i.e., Principal + Interest of 6 years = ` 4,050 ... (2)
Subtract equation (1) from equation (2) to get:
Interest of 2 years = ` (4,000 – 3,825) = ` 225
225
Interest of 1 year = ` 2 = ` 112.50
∴ Interest of 4 years = ` 112.50 × 4 = ` 450
Using equation (1),
Principal = ` 3,825 – ` 450 = ` 3,375
P = ` 3,375, I (of 1 year) = ` 112.50, T = 1 year
112.50 × 100 1  I × 100 
∴ Rate = 3,375 × 1 = 3 % per annum   Using Rate = P T×  
3

Example 5: A man invested ` 7,800 at the rate of 5% per annum, and ` 6,500 at the rate of 3% per annum
at the same time. At the end of the time period, the total interest of the two investments is
` 5,850. Find the time period of his investment.
Solution: Let the time period of the investments be x years.
7,800× 5 × x
Interest on ` 7,800 at the rate of 5% in x years = ` 100 = ` 390x
6,500× 3 × x
Interest on ` 6,500 at the rate of 3% in x years = ` 100 = ` 195x

∴ Total interest of two investments Try These
= ` 390x + ` 195x = ` 585x
According to the question, Find the interest and the amount on:
(a) ` 850 in 3 years 4 months at 10% annum.
5,850
1
585x = 5,850 ⇒ x = 585 ⇒ x = 10 (b) ` 4,000 in 1 years at 2 paise per rupee
3
Thus, the duration of investment is 10 years. per month.

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