The interest earned on Rs. 3,675 at the rate of 4% simple interest per annum for 2 years will be?
Rs. 294
Calculating Simple Interest on Principal Amount
This problem asks us to calculate the simple interest earned on a given principal amount at a specific rate for a certain period. Simple interest is calculated only on the principal amount, unlike compound interest, where interest is calculated on the principal plus accumulated interest.
Understanding the Simple Interest Formula
The formula for calculating Simple Interest (SI) is:
$$SI = \frac{P \times R \times T}{100}$$
Where:
- $$P$$ = Principal amount (the initial amount of money)
- $$R$$ = Rate of interest per annum (in percentage)
- $$T$$ = Time period (in years)
Applying the Formula to the Given Problem
We are given the following values:
- Principal (P) = Rs. 3,675
- Rate of Interest (R) = 4% per annum
- Time Period (T) = 2 years
Now, let's substitute these values into the simple interest formula:
$$SI = \frac{3675 \times 4 \times 2}{100}$$
First, multiply the numbers in the numerator:
$$3675 \times 4 = 14700$$
Then, multiply the result by the time period:
$$14700 \times 2 = 29400$$
So the numerator is 29400. Now, divide this by 100:
$$SI = \frac{29400}{100}$$
$$SI = 294$$
The simple interest earned is Rs. 294.
Summary of Calculation Steps
| Step | Description | Calculation |
|---|---|---|
| 1 | Identify Principal (P), Rate (R), Time (T) | P = 3675, R = 4%, T = 2 years |
| 2 | Write the Simple Interest formula | $$SI = \frac{P \times R \times T}{100}$$ |
| 3 | Substitute the values into the formula | $$SI = \frac{3675 \times 4 \times 2}{100}$$ |
| 4 | Calculate the numerator | $$3675 \times 4 \times 2 = 29400$$ |
| 5 | Divide the numerator by 100 | $$SI = \frac{29400}{100} = 294$$ |
The simple interest earned is Rs. 294.
Revision Table: Simple Interest Key Terms
| Term | Abbreviation | Definition |
|---|---|---|
| Principal | P | The initial sum of money invested or borrowed. |
| Rate | R | The percentage at which interest is charged or earned per period (usually annually). |
| Time | T | The duration for which the money is invested or borrowed, usually in years. |
| Simple Interest | SI | Interest calculated only on the principal amount. |
| Amount | A | The total sum including principal and interest ($$A = P + SI$$). |
Additional Information on Interest Calculations
Understanding simple interest is fundamental before moving on to more complex topics like compound interest. Here's a brief look at related concepts:
- Compound Interest: In compound interest, interest is calculated on the principal amount as well as on the accumulated interest of previous periods. This leads to a faster growth of the investment or debt compared to simple interest. The formula for compound interest is $$A = P(1 + \frac{R}{100})^T$$, where A is the amount after T years.
- Calculating Principal, Rate, or Time: The simple interest formula can be rearranged to find any of the variables (P, R, or T) if the other variables and the simple interest amount are known. For example, $$P = \frac{SI \times 100}{R \times T}$$.
- Difference between Simple and Compound Interest: The main difference lies in how interest is calculated in subsequent periods. Simple interest is constant for each period, while compound interest grows over time because it includes interest on interest.
Simple interest calculations are commonly used in some specific financial products or for basic lending scenarios over short periods.
Similar Questions
At 5% simple interest per annum a certain sum yields a total amount of ₹2,790 at the end of 3\(\frac{1}{4}\) years. The sum invested was:
Saathi deposited Rs. 825 in a bank that promised 8% simple interest per annum. If Saathi kept the money with the bank for 5 years, she will earn an interest of:
- ₹ x invested at 9% simple interest per annum for 5 years yields the same interest as that on ₹ y invested at 7.5% simple interest per annum for 4 years. Find x ∶ y.
A sum of money invested for 2 years and 9 months at the rate of 8% simple interest per annum became Rs. 732 at the end of the period. What was the sum that was initially invested?
The simple interest on a certain sum for 3 years at 8% p.a is Rs. 90 more than simple interest at 9% p.a for 2 years on the same sum. The sum is (in rupees):
A sum of money was invested at the rate of 7.5% simple interest per annuum for 4 years. If the investments were for 5 years, the interest earned would have been Rs. 375 more. What was the initial sum invested?
Rs. 750 invested for 3 months gave an interest of Rs. 18. What was the simple rate of interest per annum?
The interest earned on Rs. 1,600 at the rate of 5% simple interest per annum for 6 years would be:
At 9.5% simple interest per annum, a sum of money became Rs. 942 in 6 years. The sum invested initially was:
At 12% simple interest per annum a sum of money becomes Rs. 295 in \(1\frac{1}{2}\) years. 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?
P borrowed an amount from Q at a simple interest of 10% p.a. At the end of the year, P paid back Rs 99000 which was 90% of what she owed. How much money did P borrow?
