Page 124 - ICSE Math 8
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Example 6: The interest on a sum lent at the rate of 12.5% per annum for a period of 24 months is equal
to 1.25 times interest on ` 2,800 at the rate of 8% per annum in 2.5 years. Find the sum.
Solution: Let the required sum be ` P.
According to the question,
P × 12.5 × 24 2,800 8 2.5 ××
100 × 12 = 1.25 100 ⇒ P = ` 2,800
The required sum is ` 2,800.
EXERCISE 11.1
1. Find the interest and amount to be paid on:
(a) ` 1,650 at the rate of 11% per annum for 4 years and 10 months.
(b) ` 28,100 at the rate of 8.4% per annum for 25 months.
(c) ` 9,250 at the rate of 14% per annum for 438 days.
2. Shyam purchased a car worth ` 4,58,000. He borrowed the money at the rate of 9.5% per annum for a
period of 3.5 years. How much amount in total will he have to pay at the end of 3.5 years?
3. Rishi borrowed ` 8,600 at the rate of 7.3% per annum for 26 weeks. How much interest will he have to
pay? (Hint: 1 year = 52 weeks)
4. The interest paid on a certain sum of money is ` 2,140 in 2.5 years at the rate of 16% per annum. Find
the sum.
5. Find the principal if the interest paid over a period of 26 months at the rate of 11% per annum is ` 1,144.
6. Find the principal if the amount paid at the end of 2 years with 20% rate of interest is ` 2,002.
R T× 20 2×
Hint A = P 1+ : ⇒ A = P 1+
100 100
7. At what rate of interest per annum will ` 1,550 give interest of ` 310 over a period of 15 months?
8. In how many years will ` 2,100 give an interest of ` 840 at the rate of 12.5% per annum?
1
9. In how many years will a sum of money give an interest of times of itself at the rate of 3% per annum?
4
10. Suyash deposited ` 21,400 at the rate of 12% for a period of 16 months and ` 16,800 at the rate of 13.5%
for a period of 21 months. Which will give him more interest and by how much?
11. Rupashi had ` 20,000 with her. She deposited 33% of it for 146 days at the rate of 3.3% and the remaining
for 219 days at the rate of 6.7%. Find the total interest she will earn.
12. Ritika gave ` 23,840 to Shivani for 30 months at the rate of 14.5% per annum. At the end of the period,
Shivani gave Ritika a cheque and ` 452 in cash. How much money did she pay by cheque?
Compound Interest
In this method, the rate of interest and the time interval for compounding are fixed. The interest is calculated
on the principal after the first time interval. Then it is compounded/added to the principal. This amount then
becomes the principal for the next time interval and so on. Compounding of interest allows a principal amount
to grow at a faster rate than simple interest.
In the compound interest method, the rate of interest and time interval are fixed but the principal varies. In other
words, if the borrower and the lender agree to a certain time interval (like a year or a half year or a quarter of
a year or monthly or daily, etc.) and the rate of interest is also fixed, then Amount (Principal + Interest) at the
end of the first time interval becomes the principal for the next time interval and so on. The total interest over
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