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 ₹).
- A sum of ₹800 becomes ₹920 in 3 years at simple interest. If interest is increased by 4%, then the amount will increase to:
- An amount becomes eight-fifth of the original amount in 5 years at what percentage rate of simple interest per annum?
- The rate at which a sum becomes 2 times of itself in 10 years at simple interest is:
- Find the simple interest (in ₹) on ₹4,000 at 7.5% per annum rate of interest deposited on 4 February 2024 and withdrawn on 5 April 2024.
- How many years will it take for an amount of ₹400 to yield ₹450 as interest at 5% per annum on simple interest?
- Vikas took a loan of ₹1,200 on simple interest that is equal to as many years as the rate of interest. If he paid ₹768 as interest at the end of the loan period, then what was the rate of interest?
- A sum of money amounts to ₹12,000 after 6 years and ₹15,000 after 9 years at the same rate of simple interest. What is the rate of interest per annum?
- What will be the amount of simple interest on ₹75,000 at the rate of $2\frac{5}{3}\%$ per annum for a period of 5 years?
- A sum of money, invested for 8 years on 5% per annum simple interest, amounted to ₹175 on maturity.
What was the sum invested?
Important Questions from Simple Interest
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
Nirav and Mehul borrowed Rs.4000 and Rs.5000 respectively for 2.5 years at the rate of x% per annum. Mehul paid Rs 125 more interest than Nirav. Find x.
If the interest on a sum of Rs.1200 is more than the interest on Rs.1000 by Rs.120 in three years, then what is the rate of interest per annum?.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates?
A sum of Rs.1200 becomes Rs.1560 at a rate of simple interest in 3 years. In how many years will the sum of Rs.800 amount to Rs.1120 at the same rate of simple interest?
