Here's how to find the rate of simple interest:
Finding Interest Earned
We are given the total amount at two different times:
- Amount after 3 years = ₹1,512
- Amount after 4.5 years = ₹1,668
The difference in amount is the simple interest earned during the time difference.
Time difference = 4.5 years - 3 years = 1.5 years
Interest earned in 1.5 years = ₹1,668 - ₹1,512 = ₹156
Calculating Simple Interest Per Year
To find the interest earned in one year, divide the interest for 1.5 years by 1.5:
Simple Interest (SI) per year = $\frac{₹156}{1.5} = \frac{₹156}{3/2} = ₹156 \times \frac{2}{3} = ₹104$
Determining the Principal Amount
Now, calculate the total simple interest earned over the first 3 years:
SI for 3 years = SI per year $\times$ 3 = ₹104 $\times$ 3 = ₹312
The principal amount is the initial sum before interest was added. Find it by subtracting the SI for 3 years from the amount after 3 years:
Principal = Amount after 3 years - SI for 3 years
Principal = ₹1,512 - ₹312 = ₹1,200
Calculating the Rate of Interest
Use the simple interest formula: SI = $\frac{P \times R \times T}{100}$, where P=Principal, R=Rate, T=Time.
We can use the details for the first 3 years:
- SI = ₹312
- P = ₹1,200
- T = 3 years
Substitute these values into the formula:
$₹312 = \frac{₹1,200 \times R \times 3}{100}$
$₹312 = ₹12 \times R \times 3$
$₹312 = 36 \times R$
Solve for R (Rate):
$R = \frac{₹312}{36}$
$R = \frac{26}{3}$
Therefore, the rate of interest is $\frac{26}{3}\%$.
Similar Questions
- Find the simple interest (in ₹) on ₹4,000 at 6.75% per annum rate of interest deposited on 21 February 2024 and withdrawn on 22 April 2024.
- Sapna invested ₹21,900 on simple interest, partly at 14% per annum and partly at 10% per annum. If she earns equal interests from the two investments after 2 years, then find the sum invested at 14% per annum (in ₹).
- Find the simple interest (in ₹) on ₹1,200 at an interest rate of 4% per month for 11 months.
- A man purchases a washing machine for $₹12,000$. He pays $₹2,000$ at first and the rest after $1\text{ year}$, on which he is charged a simple interest at the rate of $10\%$ per year. The total amount he pays for the washing machine is:
- Sapna invested ₹21,700 on simple interest, partly at 3% per annum and partly at 12% per annum. If she earns equal interests from the two investments after 7 years, then find the sum invested at 3% per annum (in ₹).
- A sum of ₹800 becomes ₹920 in 3 years at simple interest. If interest is increased by 4%, then the amount will increase to:
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 4 February 2024 and withdrawn on 5 April 2024.
- Sapna invested ₹20,300 on simple interest, partly at the rate of 8% per annum and partly at the rate of 6% per annum. If she earns equal interests from the two investments after 6 years, then find the sum invested at the rate of 8% per annum (in ₹).
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 5 February 2024 and withdrawn on 6 April 2024.
- What sum of money (in ₹) will amount to ₹2,400 at 5% per annum simple interest in 4 years?
Important Questions from Simple Interest
Anil lent a sum of Rs. 5,000 on simple interest for 10 years in such a way that the rate of interest is 6% per annum for the first 2 years, 8% per anmum for the next 2 years and 10% per annum beyond 4 years. How much interest (in Rs.) will he earn at the end of 10 years?
What will be the simple interest on a sum of Rs. 12000 at the rate of 15 percent per annum for three years ?
If in 13 years fixed sum doubles at simple interest, what will be the interest rate per year? (correct to two decimal places)
On simple interest a sum of Rs. 640 becomes Rs. 832 in 2 years. What will Rs. 860 become in 4 years at the same rate of simple interest?
A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
