If ₹12,800 is invested in a bank for 5 years at the rate of 9% per annum simple interest. what amount is returned by the bank?
₹18,560
Calculating Simple Interest and Total Amount
This problem requires us to calculate the simple interest earned on a principal amount and then find the total amount returned by the bank after a specific period.
Understanding the Terms
- Principal (P): The initial amount of money invested or borrowed. In this case, it is ₹12,800.
- Rate of Interest (R): The percentage at which interest is charged or earned per annum. Here, it is 9% per annum.
- Time (T): The duration for which the money is invested or borrowed. Here, it is 5 years.
- Simple Interest (SI): The interest calculated only on the principal amount for the entire duration.
- Amount: The total sum of the principal and the interest earned. This is what is returned by the bank.
Formula for Simple Interest
The formula to calculate Simple Interest is:
\(SI = \frac{P \times R \times T}{100}\)
Step-by-Step Calculation of Simple Interest
Given:
- Principal (P) = ₹12,800
- Rate (R) = 9% per annum
- Time (T) = 5 years
Substitute these values into the Simple Interest formula:
\(SI = \frac{12800 \times 9 \times 5}{100}\)
\(SI = \frac{12800 \times 45}{100}\)
Cancel out the two zeros from the numerator and the denominator:
\(SI = 128 \times 45\)
Now, calculate the product:
\(128 \times 45 = 5760\)
So, the Simple Interest earned is ₹5,760.
Calculating the Total Amount Returned
The total amount returned by the bank is the sum of the principal and the simple interest.
Amount = Principal + Simple Interest
Amount = ₹12,800 + ₹5,760
Amount = ₹18,560
Therefore, the bank returns ₹18,560 after 5 years.
Comparing this result with the given options, we find that the correct amount is ₹18,560.
Revision Table: Simple Interest Concepts
| Term | Symbol | Definition | Formula Used Here |
|---|---|---|---|
| Principal | P | Initial amount invested/borrowed | ₹12,800 |
| Rate | R | Interest percentage per annum | 9% |
| Time | T | Duration of investment/loan | 5 years |
| Simple Interest | SI | Interest on principal only | \(SI = \frac{P \times R \times T}{100}\) |
| Amount | A | Total sum returned/paid | A = P + SI |
Additional Information: Simple vs. Compound Interest
It's important to distinguish between simple interest and compound interest.
- Simple Interest: As calculated above, the interest is calculated only on the original principal amount. The interest earned does not get added to the principal for calculating future interest.
- Compound Interest: In compound interest, the interest earned in each period is added to the principal for the next period's calculation. This means interest is earned on the interest as well as the principal, leading to faster growth of the amount over time compared to simple interest for the same rate and time.
This question specifically deals with simple interest, making the calculation straightforward based on the initial principal.
Important Questions from Simple Interest
Somu has borrowed ₹10,000 from a money lender with simple interest at a rate of 7% half yearly. How much amount will he pay to the money lender after 3 years?
Find the Simple interest on Rs. 2,400 from 20 March 2019 to 31 may 2019 at \(6{1 \over 4}\) % rate?
If the simple interest for five years is equal is 35% of the principal, that rate of interest is:
A sum fetched a simple interest of Rs. 3,040 at the rate of 8% p.a in 5 years. what is the sum?
In how many years, a sum will be thrice of it at the rate of interest 5% per annum?
