What is the amount of money invested after 4 years at the rate of simple interest rate of 13% per annum invested at 4,950 rupees. (In rupees)
7,524
Understanding Simple Interest Calculation
This question asks us to find the total amount of money after 4 years when a certain amount is invested at a simple interest rate. Let's break down the calculation step by step.
What is Simple Interest?
Simple interest is a quick and easy method of calculating the interest charge on a loan or investment. It is calculated only on the initial principal amount.
The formula for simple interest is:
$\text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100}$
Where:
- P is the initial amount of money invested (Principal).
- R is the annual rate of interest (Rate).
- T is the time the money is invested or borrowed for, in years (Time).
Calculating the Simple Interest
From the question, we are given:
- Principal (P) = 4,950 rupees
- Rate (R) = 13% per annum
- Time (T) = 4 years
Now, let's plug these values into the simple interest formula:
$\text{SI} = \frac{4950 \times 13 \times 4}{100}$
$\text{SI} = \frac{4950 \times 52}{100}$
To simplify the calculation, we can multiply 4950 by 52:
$4950 \times 52 = 257400$
Now, divide by 100:
$\text{SI} = \frac{257400}{100} = 2574$
So, the simple interest earned after 4 years is 2,574 rupees.
Calculating the Total Amount
The question asks for the total amount of money invested after 4 years. This total amount is the sum of the initial principal and the simple interest earned.
$\text{Amount} = \text{Principal} + \text{Simple Interest}$
Using the values we have:
$\text{Amount} = 4950 + 2574$
$\text{Amount} = 7524$
The total amount of money after 4 years is 7,524 rupees.
Summary of Calculation
| Variable | Value |
|---|---|
| Principal (P) | 4,950 rupees |
| Rate (R) | 13% |
| Time (T) | 4 years |
| Simple Interest (SI) | 2,574 rupees |
| Total Amount | 7,524 rupees |
The amount of money invested after 4 years at a simple interest rate of 13% per annum on an initial investment of 4,950 rupees is 7,524 rupees.
Revision Table: Simple Interest Concepts
| Concept | Description | Formula |
|---|---|---|
| Principal | The initial amount invested or borrowed. | P |
| Rate | The percentage at which interest is calculated per year. | R (as a percentage) |
| Time | The duration for which the money is invested/borrowed. | T (in years) |
| Simple Interest | Interest calculated only on the principal amount. | $\frac{P \times R \times T}{100}$ |
| Amount | The total sum including principal and interest. | Principal + Simple Interest |
Additional Information: Simple vs. Compound Interest
It's important to distinguish simple interest from compound interest. While simple interest is calculated only on the principal, compound interest is calculated on the principal amount and also on the accumulated interest from previous periods.
- Simple Interest: Interest remains constant each period based on the initial principal.
- Compound Interest: Interest for each period is calculated on the principal plus any interest earned up to that point. This leads to faster growth of the investment or debt.
The question specifically states "simple interest rate," so we correctly used the simple interest formula.
Important Questions from Interest
Three years ago, the value of a flat was Rs. 65,00,000. Its value depreciated at the rate of 5%, 4% and 3% at the end of the first, the second and the third year, respectively. What is its present value?
An electric bulb was bought at Rs. 4200 Its value depreciates at the rate of 8% per annum Its value after one year will be:
A certain sum of money amounts to \(\frac{3}{2}\) of itself in 2 years applying simple interest. Find the rate of simple interest per annum.
A sum of Rs. 2000 will become Rs. 2400 in 12 months at some rate of simple interest. Find the rate of interest per annum.
A mobile phone bought for Rs. 25000. The value of that mobile phone depreciates by 5% per annum due to its use. The value of the mobile phone after 2 years is:
