Problems on Compound Interest
Q1. Find the compound interest on Rs. 5000 at 6% per annum for 2 years.
(a) 602
(b) 618
(c) 653
(d) 669
Answer: (b) 618
Here P = Rs. 5000 , r = 6% , t = 2 years
| ∴ Amount = P ( 1 + | r | ) t |
| 100 |
| = 5000 (1 + | 6 | ) 2 |
| 100 |
| = 5000 X | 106 | X | 106 |
| 100 | 100 |
= 5618
∴ Compund Interest = Rs (5618 - 5000) = Rs 618
Q2. The difference between the simple interest and the compond interest on Rs 4000 at 10% per annum for 2 years is
(a) 20
(b) 30
(c) 40
(d) 50
Answer: (c) 40
| Simple Interest = Rs. | 4000 X 10 X 2 | = Rs. 8000 |
| 100 |
| Compound Interest = Rs. { 4000 ( 1 + | 10 | ) 2 - 4000 } |
| 100 |
| = Rs. { 4000 X | 11 | X | 11 | - 4000 } |
| 10 | 10 |
= Rs. (4840 - 4000)
= Rs. 840
∴ Difference = Rs. (840 - 800)
= Rs. 40
Q3. The difference between compound interest and simple interest on Rs. 8000 at 5 % per annum for 3 years is
(a) 57
(b) 61
(c) 65
(d) 69
Answer: (b) 61
| Simple Interest = | 8000 X 5 X 3 | = 1200 |
| 100 |
| Compound Interest = Rs. { 8000 ( 1 + | 5 | ) 3 - 8000 } |
| 100 |
| = Rs. { 8000 ( | 105 | )3 | - 8000 } |
| 100 |
| = Rs. { 8000 X | 21 | X | 21 | X | 21 | - 8000 } |
| 20 | 20 | 20 |
= Rs. (9261 - 8000) = Rs. 1261
∴ C.I - S.I = Rs. (1261 - 1200)
= Rs. 61
Q4. A tree increases annually by 1/16 of its height. By how much it increases after 2 years if it stands today 32 cm heigh ?
(a) 21.10 cm
(b) 24.26 cm
(c) 32.13 cm
(d) 36.12 cm
Answer: (d) 36.12 cm
For the first year, the height of the tree is = 32 + 32 X (1/16) cm
=32 + 2 cm = 34 cm
For the 2nd year, the of the tree is = 34 + 34 X (1/16) cm
= 34 + 2.12 cm
= 36.12 cm
Q5. What will be the compound interest on Rs. 24000 after 2 years at 10% per annum
(a) 5000
(b) 5015
(c) 5040
(d) 5045
Answer: (c) 5040
Here P = 24000 , t = 2 years, r = 10%
| ∴ Compound Interest = { 24000 ( 1 + | 10 | )2 } - 24000 |
| 100 |
| = 24000 X | 110 | X | 110 | - 24000 |
| 100 | 100 |
= 240 X 121 - 24000
= 29040 - 24000
= 5040
Q6. How much would a sum of Rs. 14000 approximately amount to in 2 years at 10 % per annum compounded half yearly
(a) 16025
(b) 16126
(c) 17017
(d) 17198
Answer: (c) 17017
Here P = Rs. 14000 , t = 4 years, r = (10/2)% = 5%
| ∴ Amount = Rs. { 14000 ( 1 + | 5 | )4 } |
| 100 |
| = Rs. { 14000 X | 105 | X | 105 | X | 105 | X | 105 | } |
| 100 | 100 | 100 | 100 |
| = Rs. { 14000 X | 21 | X | 21 | X | 21 | X | 21 | } |
| 20 | 20 | 20 | 20 |
= Rs. 17017 (approx)
Q7. The difference between compound interest and simple interest at the same rate on Rs. 5000 for 2 years is Rs. 72. The rate of interest per annum is
(a) 12 %
(b) 16 %
(c) 17 %
(d) 19 %
Answer: (a) 12 %
C.I - S.I = 70
| ⇒ { 5000 ( 1 + | r | )2 - 5000 } - | 5000 X r X 2 | =72 |
| 100 | 100 |
| ⇒ { 5000 ( | 100 + r | )2 - 5000 } - 100r | = 72 |
| 100 |
| ⇒ 5000 { ( | 100 + r | )2 - 1 } - 100r | = 72 |
| 100 |
| ⇒ 5000 X | 10000 + 200r + r2 - 10000 | - 100r | = 72 |
| 10000 |
| ⇒ 5 X | 200r + r2 | - 100r | = 72 |
| 10 |
| ⇒ | 200r + r2 - 200r | = 72 |
| 2 |
| ⇒ | r2 | = 72 |
| 2 |
⇒ r2 = 144
⇒ r = 12 %
Q8. The effective annual rate of interest, corresponding to a nominal rate of 4% per annum,payable half yearly is
(a) 2.30 %
(b) 3.45 %
(c) 4.04 %
(d) 5.12 %
Answer: (c) 4.04 %
Let, the sum be Rs. 100
Now, P = Rs. 100, r = 2%, t = 2
| ∴ Amount = 100 ( 1 + | 2 | )2 |
| 100 |
| = 100 X | 102 | X | 102 |
| 100 | 100 |
=Rs. 104.04
∴ Effective annual rate = 4.04%
Q9. A man deposited Rs. 8000 in a bank at 5% per annum simple interest. Another man deposited Rs. 6000 at 6% per annum compound interest. After 2 years the difference of their interest will be
(a) 20 Rs
(b) 25 Rs
(c) 31 Rs
(d) 35 Rs
Answer: (a) 20 Rs
| S.I = Rs. | 8000 X 5 X2 | = Rs. 800 |
| 100 |
| C.I = Rs. { 8000 (1 + | 5 | )2 - 8000 } |
| 100 |
| = Rs. { 8000 X | 105 | X | 105 | - 8000 } |
| 100 | 100 |
= Rs. {8820 - 8000}
= Rs. 820
∴ C.I - S.I = Rs. (820 - 800) = Rs. 20
Q10. A sum of money placed at compound interest doubles itself in 5 years. In how many years, it would amount to 8 times of itself at the same rate of interest ?
(a) 8 years
(b) 10 years
(c) 13 years
(d) 15 years
Answer: (d) 15 years
Let, the sum be Rs x
| Now, x (1 + | r | )5 = 2x |
| 100 |
| ⇒ ( 1 + | r | )5 = 2 -------> (1) |
| 100 |
Let, the required time t
| ∴ x (1 + | r | )t = 8x |
| 100 |
| ⇒ (1 + | r | )t = 8 |
| 100 |
| ⇒ (1 + | r | )t = 23 |
| 100 |
| ⇒ (1 + | r | )t = {(1 + | r | )5 }3 -------- From (1) |
| 100 | 100 |
⇒ t = 15 years
Practice Test Exam