Frank Solutions for Chapter 3 Compound Interest Class 9 Mathematics ICSE
1. Find the amount and the compound interest payable annually on the following:
(i) Rs 25000 for 1.1/2 years at 10% per annum.
(ii) Rs 32000 for 2 years at 7.1/2 % per annum.
(iii) Rs 10000 for 2.1/2 years at 6% per annum.
(iv) Rs 24000 for 1.1/2 years at 7.1/2% per annum.
Answer
(i) Rs 25000 for 1.1/2 years at 10% per annum.
Here,
P = Rs 25000, t = 1.1/2 years, r = 10%
Now,
Amount after 1 year = P (1 + r/100)
= 25000 (1 + 10/100)
= 25000 (1 + 1/10)
On further calculation, we get,
= 25000 (11/10)
= 27500
Hence, principle for the next 6 months = Rs 27500
Interest for the next 6 months = (27500 × 6 × 10)/(100 × 12)
= 1375
Hence, amount after 1.1/2 years = Rs 27500 + Rs 1375
= Rs 28875
And CI = A – P
= Rs 28875 – Rs 25000
= Rs 3875
(ii) Rs 32000 for 2 years at 7.1/2% per annum.
Here,
P1 = Rs 32000 and r = 7.1/2 % = (15/2)%
So, Amount after 1 year = P (1 + r/100)
= 32000 {1 + 15/(2 × 100)}
= 32000 (1 + 3/40)
= 32000 (43/40)
We get,
= 34400
Therefore,
P2 = Rs 34400 and r = (15/2)%
So, Amount after 2 year = P (1 + r/100)
= 34400 {1 + 15/(2 × 100)}
On further calculation, we get,
= 34400 (1 + 3/40)
= 34400 (43/40)
We get,
= 36980
Hence, Amount = Rs 36980
And CI = A – P
= Rs 36980 – Rs 32000
We get,
= Rs 4980
(iii) Rs 10000 for 2.1/2 years at 6% per annum.
Here,
P1 = Rs 10000 and r = 6%
So, Amount after 1 year = P (1 + r / 100)
= 10000 (1 + 6/100)
= 10000 (106/100)
On simplification, we get,
= 10600
Hence, P2 = Rs 10600 and r = 6%
Amount after 2 year = P (1 + r/100)
= 10600 (1 + 6/100)
= 10600 (106/100)
On simplification, we get,
= Rs 11236
Hence, principle for the next 6 months = Rs 11236
Interest for the next 6 months = (11236 × 6 × 6)/(100 × 12)
= 337.08
Hence, amount after 1.1/2 years = Rs 11236 + Rs 337.08
= Rs 11573.08
And CI = A – P
= Rs 11573.08 – Rs 10000
= Rs 1573.08
(iv) Rs 24000 for 1.1/2 years at 7.1/2 % per annum.
Here,
P = Rs 24000, t = 1.1/2 years, r = 7.1/2 = (15/2)%
Now,
Amount after 1 year = P (1 + r/100)
= 24000 {1 + 15/(2 × 100)}
= 24000 (1 + 3/40)
= 24000 (43/40)
We get,
= 25800
Hence, principle for the next 6 months = Rs 25800
Interest for the next 6 months = (25800 × 15 × 6)/(200 × 12)
= 967.50
Hence, amount after 1.1/2 years = Rs 25800 + Rs 967.50
= 26767.50
And CI = A – P
= Rs 26767.50 – Rs 24000
= Rs 2767.50
2. Find the amount and the compound interest payable annually on:
(a) Rs 16000 for 2 years at 15% and 12% for the successive years.
(b) Rs 17500 for 3 years at 8%, 10% and 12% for the successive years
Answer
(a) For first year: P = Rs 16000, R = 15% and T = 1 year
Therefore, interest = Rs (16000× 15 × 1)/100
= Rs 2400
And, amount = Rs 16000 + Rs 2400
= Rs 18400
For second year: P = Rs 18400, R = 12% and T = 1 year
Therefore, interest = Rs (18400 × 12 × 1)/100
= Rs 2208
And, amount = Rs 18400 + Rs 2208
= Rs 20608
Hence, required amount = Rs 20608
And, Compound Interest = A – P
= Rs 20608 – Rs 16000
We get,
= Rs 4608
(b) For first year: P = Rs 17500, R = 8% and T = 1 year
Therefore, interest = Rs (17500 × 8 × 1)/100
= Rs 1400
And, amount = Rs 17500 + Rs 1400
= Rs 18900
For second year: P = Rs 18900, R = 10% and T = 1 year
Therefore, interest = Rs (18900 × 10 × 1)/100
= Rs 1890
And, amount = Rs 18900 + Rs 1890
= Rs 20790
For third year: P = Rs 20790, R = 12% and T = 1 year
Therefore, interest = Rs (20790 × 12 × 1)/100
= Rs 2494.80
And, amount = Rs 20790 + Rs 2494.80
= Rs 23284.80
Hence, required amount = Rs 23284.80
And, Compound Interest = A – P
= Rs 23284.80 – Rs 17500
= Rs 5784.80
3. Calculate the amount and compound interest on Rs 20000 for 3 years at 10% per annum, interest being payable annually.
Answer
Here,
P1 = Rs 20000 and r = 10%
So, amount after 1 year = P (1 + r/100)
= 20000 (1 + 10/100)
= 20000 (110/100)
We get,
= 22000
Hence, P2 = Rs 22000 and r = 10%
Amount after 2 year = P (1 + r/100)
= 22000 (1 + 10/100)
= 22000 (110/100)
We get,
= 24200
Hence, P3 = Rs 24200 and r = 10%
Amount after 3 year = P (1 + r/100)
= 24200 (1 + 10/100)
= 24200 (110/100)
We get,
= 26620
Therefore, amount = Rs 26620
Also, CI = A – P
= Rs 26620 – Rs 20000
= Rs 6620
4. Compute the compound interest for the third year on Rs 5000 invested for 5 years at 10% per annum, the interest being payable annually.
Answer
For first year: P = Rs 5000, R = 10% and T = 1 year
Therefore, interest = Rs (5000 × 10 × 1)/100
= Rs 500
And, amount = Rs 5000 + Rs 500
= Rs 5500
For second year: P = Rs 5500, R = 10% and T = 1 year
Therefore, interest = Rs (5500 × 10 × 1)/100
= Rs 550
And, amount = Rs 5500 + Rs 550
= Rs 6050
For third year: P = Rs 6050, R = 10% and T = 1 year
Therefore, interest = Rs (6050 × 10 × 1)/100
= Rs 605
Hence, Compound Interest for third year is Rs 605
5. Rakesh invests Rs 25600 at 5% per annum compound interest payable annually for 3 years. Find the amount standing to his credit at the end of the second year.
Answer
For first year: P = Rs 25600, R = 5% and T = 1 year
Therefore, interest = Rs (25600 × 5 × 1)/100
= Rs 1280
And, amount = Rs 25600 + Rs 1280
= Rs 26880
For second year: P = Rs 26880, R = 5% and T = 1 year
Therefore, interest = Rs (26880 × 5 × 1)/100
= Rs 1344
And, amount = Rs 26880 + Rs 1344
= Rs 28224
Therefore, amount at the end of second year is Rs 28224
6. Find the amount and compound interest on Rs 7500 for 1.1/2 years at 8%, payable semi-annually.
Answer
Here,
P1 = Rs 7500 and rate of interest for half year (r) = 4%
So, amount after half year = P (1 + r/100)
= 7500 (1 + 4/100)
= 7500 (104/100)
We get,
= 7800
Hence, P2 = Rs 7800 and r = 4%
Amount after 1 year = P (1 + r/100)
= 7800 (1 + 4/100)
= 7800 (104/100)
We get,
= 8112
Hence, P3 = Rs 8112 and r = 4%
Amount after 1.1/2 year = P (1 + r/100)
= 8112 (1 + 4/100)
= 8112 (104/100)
We get,
= 8436.48
Therefore, amount = Rs 8436.48
Also, CI = A – P
= Rs 8436.48 – Rs 7500
= Rs 936.48
7. A man invests Rs 24000 for two years at compound interest, if his money amounts to Rs 27600 after one year, find the amount at the end of second year.
Answer
Amount after 1 year = P (1 + r/100)
27600 = 24000 (1 + r/100)
(1 + r/100) = 27600/24000
We get,
(1 + r/100) = 23/20
On further calculation, we get,
r/100 = (23/20) – 1
We get,
r/100 = 3/20
r = (100 × 3)/20
r = 15
Amount after 2 year = P (1 + r/100)
= 27600 {1 + (15/100)}
= 27600 (115/100)
We get,
= 31740
Therefore, the amount at the end of second year is Rs 31740
8. How much will Rs 14000 amounts to 2 years at compound interest, if the rates for the successive years be 5% and 8% respectively?
Answer
Here,
P1 = Rs 14000 and r = 5%
So, Amount after 1 year = P (1 + r/100)
= 14000 (1 + 5/100)
= 14000 (105/100)
We get,
= 14700
Hence, P2 = Rs 14700 and r = 8%
Amount after 2 year = P (1 + r/100)
= 14700 (1 + 8/100)
= 14700 (108/100)
We get,
= 15876
Therefore, amount = Rs 15876
9. Find the amount and the compound interest on the following:
(i) Rs 8000 for 3 years at 10% per annum compounded annually
(ii) Rs 15000 for 2 years at 8% per annum compounded semi-annually
(iii) Rs 12000 for 1.1/2 years at 5% per annum compounded annually
(iv) Rs 25000 for 2 years at 6% per annum compounded semi-annually
(v) Rs 16000 for 3 years at 10%, 8% and 6% for successive years
Answer
(i) Rs 8000 for 3 years at 10% per annum compounded annually
Here,
P = Rs 8000, t = 3 years, r = 10%
Now,
Amount = P (1 + r/100)t
= 8000 (1 + 10/100)3
= 8000 (11/10)3
= 8000 × (1331/1000)
We get,
= 10648
Therefore, amount = Rs 10648
Also, CI = A – P
= Rs 10648 – Rs 8000
= Rs 2648
(ii) Rs 15000 for 2 years at 8% per annum compounded semi-annually
Here,
P = Rs 15000, t = 2 years, r = 8%
Since interest is compounded semi-annually, so
Amount = P (1 + r/200)2t
= 15000 (1 + 8/200)4
= 15000 (26/25)4
= 15000 × (26/25) × (26/25) × (26/25) × (26/25)
On simplification, we get,
= 17547.88
Therefore, amount = Rs 17547.88
Also, CI = A – P
= Rs 17547.88 – Rs 15000
= Rs 2547.88
(iii) Rs 12000 for 1.1/2 years at 5% per annum compounded annually
Here,
P = Rs 12000, t = 1.1/2 years, r = 5%
Now,
Amount after 1 year = P (1 + r/100)t
= 12000 (1 + 5/100)
On simplification, we get,
= 12000 (105/100)
= 12600
Now, interest for the next half year = (12600 × 5)/(100 × 2)
= 315
Therefore, amount = Rs 12600 + Rs 315
= Rs 12915
Also, CI = A – P
= Rs 12915 – Rs 12000
= Rs 915
(iv) Rs 25000 for 2 years at 6% per annum compounded semi-annually
Here,
P = Rs 25000, t = 2 years, r = 6%
Since interest is compounded semi-annually,
Amount = P (1 + r/200)2t
= 25000 (1 + 6/200)4
= 25000 (103/100)4
On simplification, we get,
= 28137.72
Hence, amount = Rs 28137.72
Also, CI = A – P
= Rs 28137.72 – Rs 25000
= Rs 3137.72
(v) Rs 16000 for 3 years at 10%, 8% and 6% for successive years
Here,
P = Rs 16000, t = 3 years, r = 10%, 8%, 6% successively
Now,
Amount = P (1 + r1/100) (1 + r2/100) (1 + r3/100)
= 16000 (1 + 10/100) (1 + 8/100) (1 + 6/100)
On simplification, we get,
= 16000 (11/10) (108/100) (106/100)
= 20148.48
Therefore, Amount = Rs 20148.48
Also, CI = A – P
= Rs 20148.48 – Rs 16000
= Rs 4148.48
10. Find the amount and compound interest on Rs 15000 in 2.1/2 years at 10% p.a. compounded annually
Answer
Here,
P = Rs 15000, t = 2.1/2 years, r = 10%
Now, Amount after 2 year = P (1 + r / 100)t
= 15000 (1 + 10/100)2
= 15000 (11/10)2
We get,
= 18150
Now, interest for the next half year = (18150 × 10)/(100 × 2)
= 907.5
Therefore, Amount = Rs 18150 + Rs 907.50
= Rs 19057.50
Also, CI = A – P
= Rs 19057.50 – Rs 15000
= Rs 4057.50
11. Find the amount on Rs 36000 in 2 years 15% p.a. compounded annually.
Answer
Here,
P = Rs 36000, t = 2 years, r = 15%
Now,
Amount = P (1 + r/100)t
= 36000 (1 + 15/100)2
= 36000 (115/100)2
We get,
= 47610
Therefore, amount = Rs 47610
12. Find the amount and compound interest on Rs 50000 in 1.1/2 years at 8% p.a. compounded half-yearly.
Answer
Here,
P = Rs 50000, t = 1.1/2 years, r = 8%
Since interest is compounded half-yearly,
So, amount = P (1 + r/200)2t
= 50000 (1 + 8/200)3
= 50000 (104/100)3
We get,
= 56243.20
Therefore, Amount = Rs 56243.20
Also, CI = A – P
= Rs 56243.20 – Rs 50000
= Rs 6243.20
13. How much will Rs 25000 amount to in 2 years at compound interest, if the rates for 1st and 2nd years be 4% and 5% p.a. respectively?
Answer
Here,
P = Rs 25000, t = 2 years, r = 4%, 5% successively
Now,
Amount = P (1 + r1/100) (1 + r2/100)
= 25000 (1 + 4/100) (1 + 5/100)
On further calculation, we get,
= 25000 (104/100) (105/100)
= 27300
Therefore, Amount = Rs 27300
14. Find compound interest on Rs 31250 for 3 years, if the rates of interest for 1st, 2ndand 3rdyears be 8%, 10% and 12% respectively.
Answer
Here,
P = Rs 31250, t = 3 years, r = 8%, 10%, 12% successively
Now,
Amount = P (1 + r1/100) (1 + r2/100) (1 + r3/100)
= 31250 (1 + 8/100) (1 + 10/100) (1 + 12/100)
On further calculation, we get,
= 31250 (108/100) (110/100) (112/100)
= 41580
Therefore, Amount = Rs 41580
15. Calculate the rate percent when Rs 28000 amount to Rs 30870 in 2 years at compounded annually.
Answer
Here,
P = Rs 28000, A = 30870, t = 2 years
Now,
Amount = P (1 + r/100)t
30870 = 28000 (1 + r/100)2
⇒ (1 + r/100)2 = (30870/28000)
We get,
(1 + r/100)2 = (441/400)
⇒ (1 + r/100)2 = (21/20)2
Hence,
(1 + r/100) = (21/20)
⇒ r/100 = (21/20) – 1
⇒ r /100 = 1/20
⇒ r = 100/20
⇒ r = 5
Therefore, rate of interest is 5%
16. Simple interest on a sum of money for 2 years at 4% is Rs 450. Find the compound interest at the same rate for 1 year if the interest is reckoned half-yearly.
Answer
17. A man borrows Rs 62500 at 8% p.a., simple interest for 2 years. He immediately lends the money out at CI at the same rate and for same time. What is his gain at the end of 2 years?
Answer
18. What sum will amount to Rs 10120 in 2 years at CI payable annually, if the rates are 10% and 15% for the successive years ?
Answer
19. Sunil borrows Rs 50,000 at 10% SI for 1.1/2 years. He immediately invests the entire amount for 1.1/2 years at 10% compounded annually. What is his gain at the end of the stipulated time, when he repays his loan?
Answer
20. The value of a mobile depreciated by 5% per year during the first two years and 10% per year during the third year. Express the total depreciation of the value of the mobile in percent during the three years.
Answer
21. A man borrows Rs 6500 at 10% per annum compound interest payable half-yearly. He repays Rs 2000 at the end of every six months. Calculate the amount outstanding at the end of the third payment. Give your answer to the nearest rupee.
Answer
22. A man borrows Rs 20000 at 10% per annum compound interest payable annually. If he repays Rs 5000 at the end of the first year and Rs 10000 at the end of the second year, how much should he pay at the end of the third year in order to clear the account ? Find the answer correct to the nearest rupee.
Answer
23. Ankita bought a gold ring worth Rs x. The value of the ring increased at 10% per year compounded annually, on which the appreciation for the first year plus the appreciation for the second year amounts to Rs 6300. Find the value of the ring.
Answer
24. Priyanka lends Rs 15,500 at 10% for the first year, at 15% for the second year and at 20% for the third year. If the rates of interest are compounded yearly, find the difference between the compound interest of the second year and the third year.
Answer
25. Samidha borrowed Rs 7500 from Shreya at 30% per annum compounded interest. After 2 years, Samidha gave Rs 10000 and a juicer to Shreya to clear the debt. Find the cost of the juicer.
Answer
Exercise 3.2
1. Find the amount and the compound interest on the following:
(i) Rs 8000 for 3 years at 10% per annum compounded annually.
(ii) Rs 15000 for 2 years at 8% per annum compounded semi-annually.
(iii) Rs 12000 for 1.1/2 years at 5% per annum compounded annually.
(iv) Rs 25000 for 2 years at 6% per annum compounded semi-annually.
(v) Rs 16000 for 3 years at 10%, 8% and 6% for successive years.
Answer
(i)
2. Find the amount and compound interest on Rs 15000 in 2.1/2 years at 10% p.a. compounded annually.
Answer
3. Find the amount on Rs 36000 in 2 years 15% p.a. compounded annually.
Answer
4. Find the amount and compound interest on Rs 50000 in 1.1/2 years at 8% p.a. compounded half-yearly.
Answer
5. How much will Rs 25000 amount to in 2 years at compound interest, if the rates for 1st and 2nd years be 4% and 5% p.a. respectively ?
Answer
6. Find compound interest on Rs 31250 for 3 years, if the rates for 1st, 2nd and 3rd years be 8%, 10% and 12% respectively.
Answer
7. Calculate the rate when Rs 28000 amount to Rs 30870 in 2 years at compounded annually.
Answer
8. In what time Rs 15625 amount to Rs 17576 at 4% p.a. compound interest ?
Answer
9. In how many years will Rs 2000 amount to Rs 2662 at 10% p.a. compound interest ?
Answer
10. The simple interest on a certain sum for 3 years at 4% is RS 600. Find the compound interest for the same sum at same percent and in the same time.
Answer
11. The compound interest payable annually on a certain sum for 2 years in Rs 40.80 and the simple interest is Rs 40. Find the sum and the rate percent.
Answer
12. The difference between simple interest and compound interest compounded annually on a certain sum is Rs 448 for 2 years at 8 percent per annum. Find the sum.
Answer
13. The difference between CI payable annually and SI on Rs 50,000 for two years is Rs 125 at the same rate of interest per annum. Find the rate of interest.
Answer
14. What principal will amount to Rs 15729 in two years, if the rate of interest for successive years are 5% and 7% respectively, the interest is being compounded annually.
Answer
15. At what rate percent will Rs 12000 yield Rs 13891.50 as compound interest in 3 years ?
Answer
16. A sum of Rs 16820 is to be divided between two girls A and B, 27 and 25 years old respectively, in such a way that, if their portions be invested at 5% per annum compound interest payable annually, they will receive equal amounts on reaching 40 years of age. What is the share of each in the original sum of money ?
Answer
