Interest Calculation: Principal, Rate, and Time
This solution explains how to calculate the simple interest earned on a deposit over a specific period.
Determine the Time Period
The time period is calculated from the deposit date (21 February 2024) to the withdrawal date (22 April 2024). Note that 2024 is a leap year, so February has 29 days.
- Days remaining in February: $29 - 21 = 8$ days
- Days in March: $31$ days
- Days in April: $22$ days
- Total days: $8 + 31 + 22 = 61$ days
- Time in years ($T$): $T = \frac{61}{366}$ years
Calculate Simple Interest
The formula for simple interest (SI) is:
$ SI = \frac{P \times R \times T}{100} $Where:
- Principal ($P$) = ₹4,000
- Rate ($R$) = 6.75% per annum
- Time ($T$) = $\frac{61}{366}$ years
Substitute the values into the formula:
$ SI = \frac{4000 \times 6.75 \times \frac{61}{366}}{100} $First, convert the rate to a fraction:
$ R = 6.75 = \frac{675}{100} = \frac{27}{4} $Now, calculate the SI:
$ SI = \frac{4000 \times \frac{27}{4} \times \frac{61}{366}}{100} $ $ SI = \frac{4000 \times 27 \times 61}{4 \times 366 \times 100} $Simplify the expression:
$ SI = \frac{10 \times 27 \times 61}{366} $ $ SI = \frac{16470}{366} $Performing the division:
$ SI = 45 $Final Interest Amount
The simple interest earned is ₹45.
Similar Questions
- 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- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 4 February 2024 and withdrawn on 5 April 2024.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?
- The simple interest on a certain sum for 3 years at 8% per annum is ₹96 more than the simple interest on the same sum for 2 years at 9% per annum. Find the sum.
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?
