Exercise 14.2
1. Compute the amount and the compound interest in each of the following by using the formulae when:
(i) Principle = Rs 3000, Rate = 5%, Time = 2 years
(ii) Principle = Rs 3000, Rate =18%, Time = 2 years
(iii) Principle = Rs 5000, Rate = 10 paise per rupee per annum, Time = 2 years
(iv)Principle = Rs 2000, Rate = 4 paise per rupee per annum, Time = 3 years
(v) Principle = Rs 12800, Rate = 712%, Time = 3 years
(vi) Principle =Rs 10000, Rate 20% per annum compounded half-yearly, Time = 2 years
(vii) Principle = Rs 160000, Rate =10 paise per rupee per annum compounded half-yearly, Time = 2 years.
Solution:
2. Find the amount of Rs 2400 after 3 years, when the interest is compounded annually at the rate of 20% per annum.
Solution:
Given:
P = Rs 2400
R = 20 % p. a
n = 3 years
We know that amount A at the end of n years at the rate R% per annum when the interest is compounded annually is given by
Thus, the required amount is Rs 4147.20.
3. Rahman lent Rs 16000 to Rasheed at the rate of 1212% per annum compound interest. Find the amount payable by Rasheed to Rahman after 3 years.
Solution:
Let us see what is given in the problem:
P = Rs 16000
R = 12.5 % per annum
n = 3 years (time)
Let us calculate the Amount A at the end of 3 years at the rate 12.5% p.a by compounding the interest is annually
A = 1600 (1.125)3
A = 22781.25
Therefore, the required A is Rs 22781.25.
4. Meera borrowed a sum of Rs 1000 from Sita for two years. If the rate of interest is 10% compounded annually, find the amount that Meera has to pay back.
Solution:
Given:
P = Rs 1000
R = 10 % p.a
n = 2 years
We know that amount A at the end of n years at the rate R% per annum when the interest is compounded annually is given by
A = 1000(1.1)2
A = 1210
Thus the required
5. Find the difference between the compound interest and simple interest. On a sum of Rs 50,000 at 10% per annum for 2 years.
Solution:
let us see what is given in the problem:
P = Rs 50000
R = 10 % per annum
n = 2 years(time)
Let us calculate the Amount A at the end of 2 years at the rate 10% p.a by compounding the interest is annually
Thus, the difference between C.I & S.I = Rs 10500 – Rs 10000 = Rs 500
6. Amit borrowed Rs 16000 at 17(1/2)% per annum simple interest. On the same day, he lent it to Ashu at the same rate but compounded annually. What does he gain at the end of 2 years?
Solution:
Amount to be paid Amit:
A = 50000 (1.175)2
A = Rs 22090
We get that:
CI = A –P = Rs.22090- Rs 16000 = Rs 6090
Amit’ s gain in the whole transaction = Rs – Rs 5600 = Rs 490
7. Find the amount of Rs 4096 for 18 months at 12(1/2)% per annum, the interest being compounded semi-annually.
Solution:
Given,
Principal = Rs. 406
8. Find the amount and the compound interest on Rs 8000 for 1(1/2) years at 10% per annum, compounded half-yearly.
Solution:
Given:
P = Rs 8000
R = 10% p.a
n = 1.5 years
when compounded half-yearly,
We have:
A = Rs 9261
Also, CI = A – P = Rs 9261 – Rs 800 = Rs 1261
9. Kamal borrowed Rs 57600 from LIC against her policy at 12 1/2% per annum to build a house. Find the amount that she pays to the LIC after 12 1/2% years if the interest is calculated half-yearly.
Solution:
let us see what is given in the problem:
P = Rs 57600
R = 12.5% per annum
n = 1.5 years(time)
To compound the interest half-yearly,
So, now we have:
A =57600(1.0625)3
A = Rs 69089.06
Therefore, the needed amount is Rs 69089.06
10. Abha purchased a house from Avas Parishad on credit. If the cost of the house is Rs 64000 and the rate of interest is 5% per annum compounded half-yearly, find the interest paid by Abha after one year and a half.
Solution:
let us see what is given in the problem:
P = Rs 64000
R = 5% per annum
n = 1.5 years(time)
Let us compound the interest half-yearly,
Now we have:
Also, CI = A – P = Rs 68921 – Rs 64000 = Rs 4921
11. Rakesh lent out Rs. 10000 for 2 years at 20% per annum, compounded annually. How much more he could earn if the interest be compounded half-yearly?
Solution:
Given ‘
Principal
Rate = 20%
Time = 2 Years
Hence,
So, Rakesh can earn = Rs. (4641-4400) = Rs 241 more
12. Romesh borrowed a sum of Rs 245760 at 12.5% per annum, compounded annually. On the same day, he lent out his money to Ramu at the same rate of interest, but compounded semi-annually. Find his gain after 2 years.
Solution:
Given:
P = Rs 245760
R = 12.5% p.a
n = 2 years
When compounded annually,
A = 245760(1.0625)4
Romesh’s gain = Rs 313203. 75 – RS 313203.75 = Rs 2163.675
13. Find the amount that David would receive if he invests Rs 8192 for 18 months at 12(1/2)% per annum, the interest being compounded half-yearly.
Solution:
Given:
P = Rs 8192
R = 12.4% p.a
n = 1.\5 years
When the interest is compound half yearly. We have:
A = 8192(1.0625)3
A = Rs 9826
Thus, the required amount is Rs 9826
14. Find the compound interest on Rs 15625 for 9 months, at 16% per annum, compounded quarterly.
Solution:
15. Rekha deposited Rs 16000 in a foreign bank which pays interest at the rate of 20% per annum compounded quarterly, find the interest received by Rekha after one year.
Solution:
Given: let us see what is given in the problem:
P = Rs 16000
R = 20 % per annum
n = 1 year(time)
Now we know:
A = 16000(1.054)4
Amount = Rs 19448.10
Also, C.I = Amount – Principal = Rs 194448.10 – Rs 16000 = Rs 3448.10
Therefore, the interest received by Rekha is Rs 3448.10 after one year.
16. Find the amount of Rs 12500 for 2 years compounded annually, the rate of interest being 15% for the first year and 16% for the second year.
Solution:
Given:
P = Rs 12500
R1 = 15% p.a
R2 = 15% p.a
Thus, the required amount is Rs 16675.
17. Ramu borrowed Rs 15625 from a finance company to buy a scooter. If the rate of interest be 16% per annum compounded annually, what payment will he have to make after 2(1/4) years?
Solution:
Given:
P = Rs 15625
R = 16% p.a
n = 2 1/2
18. What will Rs 125000 amount to at the rate of 6%, if the interest is calculated after every four months?
Solution:
let us calculate the Compound interest every 3 months(quarterly)
let us see what is given in the problem:
P = Rs 125000
R = 6% p.a = quarterly = 1.5% quarterly
n = 3
A = 125000 (1.015)3
A = Amount = Rs 1326670 approx
Therefore, the required amount (A) is Rs 132670.
19. Find the compound interest at the rate of 5% for three years on that principal which in three years at the rate of 5% per annum gives Rs. 12000 as simple interest.
Solution:
Given,
Simple interest = Rs. 12000
Rate = 5% per annum
Time = 3 years
So,
20. A sum of money was lent for 2 years at 20% compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs 482 more. Find the sum.
Solution:
Thus, CI = 1.4641y – y = 0.4641y …..(2)
if interest is compounded half-yearly, then it will be Rs 482 more.(Given)
therefore, 0.4641y = 0.44y + 482 [From (1) and (2)]
0.4641y – 0.44y = 482
0.0241y = 482
Therefore, the required sum is Rs 20000.
21. Simple interest on a sum of money for 2 years at per annum is Rs 5200. What will be the compound interest on the sum at the same rate for the same period?
Solution:
A = 40000(1.065)2
Amount = Rs 45369
And, CI = A – P = Rs 45369 – Rs 40000 = Rs 5369
Therefore, the required C.I is Rs 5369.
22. Find the compound interest at the rate of 5% per annum for 3 years on that principle which in 3 years at the rate of 5% per annum gives Rs 1200 as simple interest.
Solution:
According to the given values, we have: