- Q. A sum of money amounts to Rs. 12,100 in 2 years and Rs. 13,310 in 3 years, when compounded annually. Find the rate of interest.
- 12%
- 9%
- 10%
- 8%
Answer is : C
Given:
Amount in 2 years = Rs.12100
Amount in 3 years = Rs.13310
Formula:
Let P = Principal, R = Rate of interest and N = time
Amount = P(1 + R/100)n
Calculation:
⇒ 12100 = P(1 + R/100)2 ----(1)
⇒ 13310 = P(1 + R/100)3 ----(2)
Dividing equation (2) by (1),
⇒ 1.1 = (1 + R/100)
⇒ 0.1 = R/100
⇒ R = 10
∴ Rate of interest is 10% per annum.
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Question: A sum of money amounts to Rs. 12,100 in 2 years and Rs. 13,310 in 3 years, when compounded annually. Find the rate of interest.
Given Answer: C
Suggestion for Correct Answer: A B C D
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Similar Questions
- 1. Find the compound interest on a sum of Rs. 2000 at 10% per annum for 1 year, compounded half-yearly.
- Rs. 200
- Rs. 150
- Rs. 205
- Rs. 155
Answer is : C
Given:
Sum = Rs. 2000
Time = 1 year
Rate = 10%
Concept used:
When the sum is compounded half-yearly, then the rate of interest becomes half and time becomes double.
Formula used:
A = P (1 + R/100)T
C.I = A - P
Where, A = Amount, P = Principal, T = Time, C.I = Compound interest and R = rate of interest
Calculation:
According to the question,
R = 10%/2 = 5%
T = 2 × 1 = 2 years
A = P (1 + R/100)T
⇒ 2000(1 + 5/100)2
⇒ 2000(1 + 1/20)2
⇒ 2000(21/20)2
⇒ 2000(441/400)
⇒ 5 × 441
⇒ 2205
C.I = 2205 - 2000
⇒ 205
∴ The compound interest is Rs. 205.
We'll use successive percentage method to solve this
Total percentage change = [a + b + (ab)/100]%, where a and b are positive percentage change
Here rate will be 10/2 = 5% (As compounded half yearly)
Total interest for 1 year compounded half yearly = [5 + 5 + (5 × 5)/100] %
⇒ Total interest = 10.25%
Compound interest = 10.25% of 2000 = 205
∴ The compound interest is Rs. 205.
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Question: Find the compound interest on a sum of Rs. 2000 at 10% per annum for 1 year, compounded half-yearly.
Given Answer: C
Suggestion for Correct Answer: A B C D
- 2. A car was bought for ? 16,000. Its value is reduced by 10% per annum. What will be the value after 2 years?
- ?12060
- ?12960
- ?12000
- ?12900
Answer is : B
Given:
Cost of a car = Rs.16000
Value reduction percentage = 10% p.a.
Formula used:
Value of car after 2 years of reduction = Cost Price × (100 - R)% × (100 - R)%
Calculation:
Value of car after 2 years = Rs.16000 × (100 - 10)/100 × (100 - 10)/100
⇒ Rs.16000 × 90/100 × 90/100
⇒ Rs.160 × 81
⇒ Rs.12960
∴ The required result is Rs.12960.
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Question: A car was bought for ? 16,000. Its value is reduced by 10% per annum. What will be the value after 2 years?
Given Answer: B
Suggestion for Correct Answer: A B C D
- 3. A sum of money doubles itself at a compound interest in 8 years. In how many years will it become four times itself?
- 12
- 20
- 14
- 16
Answer is : D
Formula:
Let P = Principal, R = rate of interest and N = time
Compound interest = P(1 + R/100)N - P
Calculation:
Let P = Rs.100 and A = Rs.200
⇒ 200 = 100(1 + R/100)8
⇒ 2 = (1 + R/100)8
Squaring both sides,
⇒ 4 = (1 + R/100)16
∴ In 16 years, it will become four times.
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Question: A sum of money doubles itself at a compound interest in 8 years. In how many years will it become four times itself?
Given Answer: D
Suggestion for Correct Answer: A B C D
- 4. Find the rate of interest if the simple interest on a principal of Rs. 1,000 gave an interest of Rs. 440 in a span of 5 years.
- 8.40%
- 8.55%
- 8.8%
- 8.9%
Answer is : C
Given:
Principal = Rs. 1000
Time = 5 years
Concept used:
S.I = PTR/100
Calculation:
Let the rate of interest be r
440 = (1000 × 5 × r)/100
⇒ 440 = 50r
⇒ 44 = 5r
⇒ 44/5 = r
⇒ r = 8.8
∴ Rate of interest is 8.8%
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Question: Find the rate of interest if the simple interest on a principal of Rs. 1,000 gave an interest of Rs. 440 in a span of 5 years.
Given Answer: C
Suggestion for Correct Answer: A B C D
- 5. Find the simple interest of 2 years of Rs. 4000 at the rate of 10% per annum
- Rs. 8
- Rs. 80
- Rs. 800
- Rs. 1600
Answer is : C
Given:
Principal = Rs.4000
Time = 2 years
Rate = 10% per annum
Concept:
Simple interest = (principal × rate × time)/100
Calculation:
We know that,
S.I. = (prt)/100
⇒ (4000 × 2 × 10)/100
⇒ Rs.800
Hence, the simple interest is Rs.800.
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Question: Find the simple interest of 2 years of Rs. 4000 at the rate of 10% per annum
Given Answer: C
Suggestion for Correct Answer: A B C D
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