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.
Important Questions from Simple Interest
Anil lent a sum of Rs. 5,000 on simple interest for 10 years in such a way that the rate of interest is 6% per annum for the first 2 years, 8% per anmum for the next 2 years and 10% per annum beyond 4 years. How much interest (in Rs.) will he earn at the end of 10 years?
What will be the simple interest on a sum of Rs. 12000 at the rate of 15 percent per annum for three years ?
If in 13 years fixed sum doubles at simple interest, what will be the interest rate per year? (correct to two decimal places)
On simple interest a sum of Rs. 640 becomes Rs. 832 in 2 years. What will Rs. 860 become in 4 years at the same rate of simple interest?
A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
