What is the simple interest on Rs. 5000 at the rate of 8% per annum for 3 years?
Answer:
Rs. 1200
The formula for simple interest is SI = (P × R × T) / 100. Here, Principal (P) is Rs. 5000, Rate (R) is 8%, and Time (T) is 3 years. Plugging the values into the formula gives SI = (5000 × 8 × 3) / 100 = 120000 / 100 = Rs. 1200.
2
If the simple interest on a certain sum of money for 4 years at 5% per annum is Rs. 800, what is the principal amount?
Answer:
Rs. 4000
Using the simple interest formula SI = (P × R × T) / 100, we can rearrange it to find the Principal (P). P = (SI × 100) / (R × T). Substituting the given values: P = (800 × 100) / (5 × 4) = 80000 / 20 = Rs. 4000.
3
At what rate percent per annum will a sum of Rs. 6000 yield Rs. 1800 as simple interest in 5 years?
Answer:
6%
To find the rate of interest, we use the formula R = (SI × 100) / (P × T). Given SI = Rs. 1800, P = Rs. 6000, and T = 5 years. Therefore, R = (1800 × 100) / (6000 × 5) = 180000 / 30000 = 6%.
4
In how many years will Rs. 2500 amount to Rs. 3250 at the rate of 6% per annum simple interest?
Answer:
5 years
First, find the simple interest earned by subtracting the principal from the total amount: SI = 3250 - 2500 = Rs. 750. Then, use the time formula T = (SI × 100) / (P × R). T = (750 × 100) / (2500 × 6) = 75000 / 15000 = 5 years.
5
A sum of money doubles itself in 10 years at simple interest. What is the rate of interest per annum?
Answer:
10%
Let the principal be P. If it doubles, the Amount A = 2P, which means the Simple Interest SI = A - P = 2P - P = P. Using the formula R = (SI × 100) / (P × T), we get R = (P × 100) / (P × 10) = 100 / 10 = 10% per annum.
6
A sum of money triples itself in 20 years at simple interest. Find the rate of interest.
Answer:
10%
Let the principal be P. If it triples, the Amount is 3P, meaning the simple interest earned is 3P - P = 2P. The rate R = (SI × 100) / (P × T) = (2P × 100) / (P × 20) = 200 / 20 = 10%.
7
If the simple interest on a certain sum is 9/16 of the principal and the number of years is equal to the rate percentage per annum, find the rate of interest.
Answer:
7.5%
Let the principal be P. SI = (9/16)P. Given that Time (T) = Rate (R). Using the SI formula: (9/16)P = (P × R × R) / 100. This gives R² = (9 × 100) / 16 = 900 / 16. Taking the square root, R = 30 / 4 = 7.5%.
8
The simple interest on a sum of money for 3 years at 4% per annum is Rs. 240. What would be the compound interest on the same sum at the same rate for 2 years?
Answer:
Rs. 163.20
First, find the principal from the SI details: P = (240 × 100) / (4 × 3) = 24000 / 12 = Rs. 2000. Now, calculate the compound interest for 2 years at 4%. Amount = P(1 + R/100)^T = 2000(1 + 4/100)² = 2000 × 1.04 × 1.04 = 2163.20. CI = Amount - Principal = 2163.20 - 2000 = Rs. 163.20.
9
Calculate the compound interest on Rs. 10000 for 2 years at 10% per annum.
Answer:
Rs. 2100
Using the compound interest formula A = P(1 + R/100)^T, the Amount A = 10000(1 + 10/100)² = 10000(1.10)² = 10000 × 1.21 = Rs. 12100. The Compound Interest (CI) is Amount - Principal = 12100 - 10000 = Rs. 2100.
10
The difference between simple interest and compound interest on a sum of money for 2 years at 5% per annum is Rs. 15. Find the sum.
Answer:
Rs. 6000
The formula for the difference between CI and SI for 2 years is D = P(R/100)². Substituting the given values: 15 = P(5/100)². This simplifies to 15 = P(1/20)² = P/400. Therefore, P = 15 × 400 = Rs. 6000.
11
What will be the compound interest on Rs. 8000 at 20% per annum for 9 months, compounded quarterly?
Answer:
Rs. 1261
When compounded quarterly, the rate is divided by 4, and time is multiplied by 4. Rate per quarter = 20% / 4 = 5%. Time = 9 months = 3 quarters. Amount A = 8000(1 + 5/100)³ = 8000(21/20)³ = 8000 × (9261 / 8000) = 9261. CI = 9261 - 8000 = Rs. 1261.
12
A sum of Rs. 12000 amounts to Rs. 13230 in 2 years. Find the rate of compound interest per annum.
Answer:
5%
Using the formula A = P(1 + R/100)^T, we have 13230 = 12000(1 + R/100)². This gives (1 + R/100)² = 13230 / 12000 = 441 / 400. Taking the square root of both sides gives 1 + R/100 = 21/20. So, R/100 = 1/20, which means R = 5%.
13
In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
Answer:
3 years
Using the compound interest formula: 1331 = 1000(1 + 10/100)^T. This simplifies to 1331 / 1000 = (11/10)^T. Since 1331 is 11³ and 1000 is 10³, we get (11/10)³ = (11/10)^T. Therefore, T = 3 years.
14
The compound interest on a certain sum for 2 years is Rs. 410 and the simple interest is Rs. 400. Find the rate of interest.
Answer:
5%
The SI for 2 years is Rs. 400, so SI for 1 year is Rs. 200. The difference between CI and SI for the second year is 410 - 400 = Rs. 10. This Rs. 10 is the interest earned on the first year's interest (Rs. 200). Rate = (10 / 200) × 100 = 5%.
15
Find the principal if the difference between the compound interest and simple interest for 3 years at 10% per annum is Rs. 31.
Answer:
Rs. 1000
The formula for the difference between CI and SI for 3 years is D = P(R/100)²(3 + R/100). Plugging in the values: 31 = P(10/100)²(3 + 10/100) = P(1/100)(3.1). Therefore, 31 = P × 0.031. Solving for P gives P = 31 / 0.031 = Rs. 1000.
16
A sum of money doubles itself at compound interest in 15 years. In how many years will it become eight times?
Answer:
45 years
For compound interest, if a sum becomes 'x' times in 'T' years, it becomes x^n times in 'n × T' years. Here, it becomes 2 times in 15 years. We want to find when it becomes 8 times, which is 2³ times. So, n = 3. Time required = 3 × 15 = 45 years.
17
A man invested 1/3 of his capital at 7%, 1/4 at 8%, and the remainder at 10%. If his annual income is Rs. 561, find the capital.
Answer:
Rs. 6600
Let the total capital be P. The remainder of the capital is 1 - (1/3 + 1/4) = 1 - 7/12 = 5/12. Total SI = (P/3 × 7/100) + (P/4 × 8/100) + (5P/12 × 10/100) = 561. This simplifies to 7P/300 + 8P/400 + 50P/1200 = 561. LCM is 1200. (28P + 24P + 50P) / 1200 = 561 => 102P = 561 × 1200 => P = Rs. 6600.
18
What sum of money will amount to Rs. 520 in 5 years and to Rs. 568 in 7 years at simple interest?
Answer:
Rs. 400
The interest earned in 2 years (from year 5 to year 7) is 568 - 520 = Rs. 48. Simple interest for 1 year is 48 / 2 = Rs. 24. Interest for 5 years is 24 × 5 = Rs. 120. Since Amount = Principal + SI, the Principal = Amount in 5 years - SI for 5 years = 520 - 120 = Rs. 400.
19
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
Answer:
12%
Interest for 3 years (8 - 5) is 12005 - 9800 = Rs. 2205. Interest for 1 year = 2205 / 3 = Rs. 735. Interest for 5 years = 735 × 5 = Rs. 3675. Principal = 9800 - 3675 = Rs. 6125. The rate R = (SI × 100) / (P × T) = (735 × 100) / (6125 × 1) = 12%.
20
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate. He received Rs. 2200 in all from both as interest. The rate of interest is:
Answer:
10%
Total SI = SI from B + SI from C. 2200 = (5000 × R × 2) / 100 + (3000 × R × 4) / 100. This simplifies to 2200 = 100R + 120R = 220R. Therefore, R = 2200 / 220 = 10% per annum.
