Exercise 14.1
1. Find the compound interest when principal = Rs 3000, rate = 5% per annum and time = 2 years.
Solution:
According to the question,
Principal amount for the first year = Rs 3,000
i.e., The amount at the end of the second year = Rs 3,150+Rs 157.50= Rs 3307.50
Therefore,
The compound interest = The amount at the end of the second year – Principal amount for the first year
=Rs 3,307.50 – 3,000
= Rs 307.50
2. What will be the compound interest on Rs 4000 in two years when the rate of interest is 5% per annum?
Solution:
Giver P = Rs 4,000
R = 5% p.a
n = 2 years
Now,
= Rs 4410
And, CI = A-P = Rs 4,410- 4,000 = Rs 410
3. Rohit deposited Rs 8000 with a finance company for 3 years at an interest of 15% per annum. What is the compound interest that Rohit gets after 3 years?
Solution:
We know that,
Amount A at the end of n years at the rate of R% per annum is given by the formula,
Giver in the question:
P = Rs 8,000
R= 15% p.a.
N = 3 years.
Substituting in the equation,
A = Rs. 12,167
Therefore, the compound interest, CI = Amount A at the end of n years – Principal amount P
= A – P
= Rs 12167 – Rs 8,000
= Rs 4,167
4. Find the compound interest on Rs. 1000 at the rate of 8% per annum for 1 years when interest is compounded half yearly.
Solution:
5. Find the compound interest on Rs 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly.
Solution:
Given:
p = Rs 160,000
R = 20 % p.a.
n = 1 year
We know that:
Now, CI = A – P = Rs 19,448.1 Rs 16,000 = Rs 3,4481
6. Swati took a loan of Rs 16000 against her insurance policy at the rate of 1212% per annum. Calculate the total compound interest payable by Swati after 3 year.
Solution:
We know that,
Amount A at the end of n years at the rate of R% per annum is given by the formula,
Therefore, the compound interest, CI = Amount A at the end of n years- Principal amount P
= A – P
= Rs 22,781.25 – Rs 16,000
= Rs 6,781.25
7. Roma borrowed Rs. 64000 from a bank for 1years at the rate of 10% per annum. Compare the total compound interest payable by Roma after 1years, if the interest is compounded half-yearly.
Solution:
Given,
Principal = Rs. 64000
8. Mewa Lal borrowed Rs 20000 from his friend Rooplal at 18% per annum simple interest. He lent it to Rampal at the same rate but compounded annually. Find his gain after 2 years.
Solution:
= 20000(1.18)2 – 20,000
= 27,848- 20,000
= Rs 7,848
i.e., Mewa Lal gained Rs 7,848 as interest after lending the money.
Therefore, his total gain= Compound Interest for the amount he lend-Simple Interest for the amount he borrowed
= Rs 7,848 – Rs 7,200
= Rs 648
9. Find the compound interest on Rs 8000 for 9 months at 20% per annum compounded quarterly.
Solution:
P = Rs 8,000
T = 9 months = 3 per quarters
R = 20% per annum = 5% per quarter
A = 8000(1.05)3
A = 9,261
The required amount is Rs 9,261.
Now,
CI = A – P = Rs 9,261 – Rs 8,000 = Rs 1,261
10. Find the compound interest at the rate of 10% per annum for two years on that principal which in two years at the rate of 10% per annum given Rs. 200 as simple interest.
Solution:
Given,
Rate of simple interest = 10%
Time = 2years
Simple interest = Rs. 200
So,
11. Find the compound interest on Rs 64000 for 1 year at the rate of 10% per compounded quarterly.
Solution:
To Calculate the interest compounded quarterly,
A = 64000 (1.025)4
A = 70,644.03
Thus,
The required amount is Rs 70,644.03.
Now, CI = A – P = Rs 70,644.025 – Rs 64,000 = Rs 64 6,644.03
12. Ramesh deposited Rs 7500 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount which he receives after 9 months?
Solution:
Given:
P = Rs 7,500
R = 12% P.A = 3% quarterly
T = 9months = 3 quarters
We know that:
A = 7500 (1.03)3
A = 8,195.45
Thus required amount is Rs 8,195.45.
13. Anil borrowed a sum of Rs 9600 to install a hand pump in his dairy. If the rate of 1 interest is % per annum compounded annually, determine the compound interest which Anil will have to pay after 3 years.
Solution:
We know that,
Amount A at the end of n years at the rate of R% per annum is given by the formula,
A = 9600 (1.055)3
A =Rs 11,272.72
Thus, the required amount =Rs 11,272.72.
Therefore, the compound interest, CI = Amount A at the end of n years- Principal amount P
=A – P
= Rs 11,272.72 – Rs 9,600
= Rs 1,672.72
14. Surabhi borrowed a sum of Rs. 12000 from a finance company to purchase a refrigerator. If the rate of interest is 5% per annum compounded annually, calculate the compound interest that Surabhi has to pay to the company after 3 years.
Solution:
Given,
Principal = Rs. 12000
Rate = 5%
Time = 3 years
Hence,
So, Compound interest paid by Surabhi to the company = Rs. 1891.50