A person borrows Rs. 5000 at 5% rate of interest per annum and immediately lent it at 5.5%. After two years he collected the amount and settled his loan. What is the amount gained by him this transaction?
Rs. 50
Calculating Profit in a Simple Interest Transaction
This problem involves understanding how simple interest works when borrowing and lending money at different rates over a period of time. A person acts as an intermediary, borrowing at one rate and lending at a slightly higher rate. The gain comes from the difference in the total interest amounts after a specific duration.
Understanding Simple Interest
Simple interest is calculated only on the principal amount. The formula for simple interest (SI) is:
\(\text{SI} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100}\)
Where:
- P = the initial amount (principal)
- R = the annual interest rate (as a percentage)
- T = the time period in years
Calculating Interest Paid
The person borrows Rs. 5000 at a 5% annual interest rate for 2 years. Let's calculate the total simple interest paid:
\(\text{Interest Paid} = \frac{5000 \times 5 \times 2}{100}\)
\(\text{Interest Paid} = \frac{50000}{100}\)
\(\text{Interest Paid} = 500\)
So, the total simple interest paid on the loan is Rs. 500.
Calculating Interest Received
The person lends the same Rs. 5000 at a 5.5% annual interest rate for 2 years. Let's calculate the total simple interest received:
\(\text{Interest Received} = \frac{5000 \times 5.5 \times 2}{100}\)
\(\text{Interest Received} = \frac{5000 \times 11}{100}\)
\(\text{Interest Received} = \frac{55000}{100}\)
\(\text{Interest Received} = 550\)
So, the total simple interest received from lending the money is Rs. 550.
Calculating the Amount Gained (Profit)
The profit or amount gained from this transaction is the difference between the total interest received and the total interest paid:
\(\text{Amount Gained} = \text{Interest Received} - \text{Interest Paid}\)
\(\text{Amount Gained} = 550 - 500\)
\(\text{Amount Gained} = 50\)
Therefore, the amount gained by the person in this transaction is Rs. 50.
Summary of Calculations
| Item | Principal (P) | Rate (R) | Time (T) | Simple Interest (SI) |
|---|---|---|---|---|
| Loan (Interest Paid) | Rs. 5000 | 5% | 2 years | Rs. 500 |
| Lending (Interest Received) | Rs. 5000 | 5.5% | 2 years | Rs. 550 |
The difference, Rs. 550 - Rs. 500 = Rs. 50, is the net gain.
Revision Table: Key Simple Interest Concepts
| Term | Definition | Formula |
|---|---|---|
| Principal (P) | The initial amount of money borrowed or lent. | - |
| Rate (R) | The percentage of interest charged or earned per period (usually per annum). | - |
| Time (T) | The duration for which the money is borrowed or lent. | - |
| Simple Interest (SI) | Interest calculated only on the principal amount. | \(\text{SI} = \frac{P \times R \times T}{100}\) |
| Amount (A) | The total money paid back (Principal + Interest). | \(A = P + SI\) |
Additional Information: Simple vs. Compound Interest
It's important to distinguish between simple interest and compound interest, although this problem uses simple interest.
- Simple Interest: Interest is calculated only on the original principal amount throughout the entire loan or investment period. The interest earned (or paid) each period does not get added back to the principal for calculating interest in the next period.
- Compound Interest: Interest is calculated on the initial principal plus all the accumulated interest from previous periods. This means that in subsequent periods, you earn (or pay) interest on interest. Compound interest leads to much faster growth of money over time compared to simple interest.
This question specifically mentions a rate of interest per annum without indicating compounding, so we correctly applied the simple interest formula.
Similar Questions
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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?
