Compound Interest problems
- 1. The cost price of an LCD TV set is ? 100000. If its price value depreciates at the rate of 10% pa. then what will be the price at the end of 3 yr?
Options- A. ? 80000
- B. ? 85000
- C. ? 90000
- D. ? 72900 Discuss
Correct Answer: ? 72900
Explanation:
Given P = ? 100000, R = 10%, n = 3 yr
According to the formula,
Price of LCD TV set after 3 yr. = P(1 - R/100)n
= 100000 (1 - 10/100)3
= 100000(90/100)3
= 100000 x (9/10) x (9/10) x (9/10)
= ? 72900
- 2. A sum, at the compound rate of interest, becomes 2 1/ 2 times in 6 yr. The same sum becomes what times in 18 yr?
Options- A. 5/2
- B. 25/4
- C. 125/8
- D. 625/16 Discuss
Correct Answer: 125/8
Explanation:
If sum is P, then P becomes 5P/2 in 6 yr.
5P/2 becomes 25P/4 in 12 yr.
25P/4 becomes 125P/8 in 18 yr.
The sum becomes 125/8 times in 18 yr.
- 3. If the difference between the compound interest and simple interest on a sum of money at 5% pa for 2 yr is ? 16, then find the simple interest?
Options- A. ? 840
- B. ? 932
- C. ? 520
- D. ? 640 Discuss
Correct Answer: ? 640
Explanation:
Given, CI - SI = 16, R = 5%, n = 2 yr and SI = ?
According to the formula,
CI - SI = (SI x R)/200
? 16 = (SI x 5)/200
? 16 = SI/40
? SI = ? 640
- 4. The compound interest is ? 6.40 more than the simple interest, if a sum is lent for 2 yr at 8% compound interest. Find the sum.
Options- A. ? 1800
- B. ? 10000
- C. ? 800
- D. ? 1000 Discuss
Correct Answer: ? 1000
Explanation:
Here, D = ?6.40, R = 8% and n = 2 yr
Then, according to the formula,
Difference between compound interest and simple interest
D = PR2 / 1002
? 6.40 = P x 64/10000
? P = ? 1000
- 5. A certain sum at compound interest amounts to ? 12960 in 2 yr and ? 13176 in 3 yr. Find the rate per cent per annum.
Options- A. 11/3%
- B. 21/3%
- C. 12/3%
- D. 22/3% Discuss
Correct Answer: 12/3%
Explanation:
SI for on ? 12960 for 1 yr
= 13176 - 12960 = ? 216
By formula, SI = (P x R x T)/ 100
? 216 = (12960 x R x 1)/100
? R = 5/3 = 12/3
- 6. The simple interest on a certain sum for 2 yr is ? 120 and compound interest is ? 129. Find the rate of interest.
Options- A. 14%
- B. 15%
- C. 12%
- D. none of the above Discuss
Correct Answer: 15%
Explanation:
Here, n = 2 yr, SI = ? 120 and CI = ? 129
CI = SI (1+ R/200)
? 129 = 120(1 + R/200)
? 129/120 = 1 + R/200
? (129/120) - 1 = R / 200
? 9/120 = R/200
? R = (9 x 200)/120 = 15%
- 7. The height of a tree increases every year 1/8 times. If the present height of the tree is 64 cm, then what will be its height after 2 yr?
Options- A. 76 cm
- B. 80 cm
- C. 81 cm
- D. 84 cm Discuss
Correct Answer: 81 cm
Explanation:
Percentage growth = (1/8) x 100 % = 12.5%
Height after 2 yr = 64 x (1+ 12.5/100)2
= 64 x (9/8) x (9/8) = 81 cm
- 8. An amount at the rate of 5% pa becomes ? 10 more at compound interest than that of simple interest after 2 yr. Calculate the principal.
Options- A. ? 4000
- B. ? 4050
- C. ? 5000
- D. ? 5500 Discuss
Correct Answer: ? 4000
Explanation:
Here, CI - SI = 10, R = 5%, n = 2 yr and P = ?
According to the formula,
CI - SI = PR2/1002
? 10 = (P x 25)/10000
? P = (400 x 10) = ? 4000
- 9. The principal amount which yields a compound interest of ? 208 in the second year at 4% is
Options- A. ? 5000
- B. ? 10000
- C. ? 130000
- D. ? 6500 Discuss
Correct Answer: ? 5000
Explanation:
Let the principal be ? P.
Amount after first year = (P x 104)/100 and
amount after second year P x (104/100) x (4/100)
According to the question.
(P x 104 x 4)/(100 x 100) = 208
? P = ? 5000
- 10. Find the compound interest for a sum of ? 9375 in 2 yr, if the rate of interest for the first year is 2% and for the second year is 4%.
Options- A. ? 570
- B. ? 670
- C. ? 770
- D. ? 760 Discuss
Correct Answer: ? 570
Explanation:
Given, P = ? 9375, R1 = 2% and R2 = 4%
According to the formula,
A = P (1 + R1/100) (1 + R2/100)
= 9375 (1 + 2/100) (1 + 4/100)
= 9375 x (51/50) x (26/25)
= 7.5 x 51 x 26
= ? 9945
Now CI = A - P = 9945 - 9375 = ? 570
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