Page 131 - ICSE Math 8

Solution: P = ` 1,000, A = ` 1,102.50, n = 2 years
Let the rate % be R.

Ê R ˆ n Ê R ˆ 2
A = P 1+ 100¯ fi 1,102.50 = 1,000 1+ 100¯
˜
Á
˜
Á
Ë
Ë
1102 5, . Ê R ˆ 2 441 Ê R ˆ 2
fi = Á 1+ ˜ fi = Á 1+ ˜
1 000, Ë 100¯ 400 Ë 100¯
Ê R ˆ 2 Ê 21ˆ 2 R 21 R 21 21 20-
fi 1+ 100¯ ˜ = Á Ë 20¯ fi 1 + 100 = 20 fi 100 = 20 – 1 = 20
Á
˜
Ë
R 1 100
fi = fi R = = 5
100 20 20
Hence, rate is 5% per annum.
EXERCISE 11.4

1. In how many years will ` 4,000 amount to ` 5,324 at the rate of 10% per annum compounded annually?
2. At what rate of compound interest will ` 1,250 amount to ` 1,800 in 2 years?
3. Anuradha invested a certain sum of money at the compound interest of 8% per annum compounded
annually. At the end of 2 years, she received an amount of ` 7,290. How much amount did Anuradha
invest?
4. If the amount after 1 1 years at the rate of 25% per annum compounded half-yearly is ` 10,935, find the
principal. 2
5. The difference between the compound interest and the simple interest on a certain principal for
1
2 years at the rate of 6 % per annum is ` 25. Find the principal.
4
6. A sum of ` 2,000 amounts to ` 2,163.20 in 2 years. Find the rate of interest if the interest is compounded
annually.
7. Find the compound interest at the rate of 5% per annum for 3 years on that principal which in 3 years at
the rate of 5% per annum gives ` 1,200 as the simple interest.
1
8. A sum of ` 31,250 amounts to ` 35,152 in 1 years. Find the rate per annum, interest being compounded
semi-annually. 2

9. Hariti invested a certain sum of money for 1 1 years at the rate of 15% per annum compounded
1 2
six-monthly. At the end of 1 years she receives a compound interest of ` 1,891.50. Find the sum
invested by Hariti. 2
10. Find the rate at which a certain sum of money will almost double itself in 2 years, if the interest is
compounded annually.
11. The difference between the compound interest and the simple interest on a sum of ` 15,000 for
2 years is ` 96. What is the rate of interest?
12. Pallavi deposited ` 46,875 in a bank. In how many years will this sum yield a compound interest of
` 5,853 at the rate of 8% per annum compound semi-annually?
13. Sanju took a loan from the bank to buy a motorcycle at the rate of 15% per annum compounded half-
1
yearly. He paid a compound interest of ` 15,507 after 1 years. Find his loan amount.
2
14. In how much time will a sum of money double if invested at the rate of 8% simple interest per annum?

119