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?
4,400
Calculating Simple Interest Over Different Periods
This problem involves calculating the total simple interest earned on a principal amount when the interest rate changes over the investment period. We need to break down the total time into segments based on the different interest rates and calculate the simple interest for each segment. The total interest will be the sum of the simple interests from all segments.
The principal amount is Rs. 5,000, and the total duration is 10 years.
The interest rates are applied as follows:
- For the first 2 years: Rate = 6% per annum
- For the next 2 years (Year 3 and Year 4): Rate = 8% per annum
- Beyond 4 years (Year 5 to Year 10): Rate = 10% per annum
Let's determine the duration for each rate period:
- Period 1: First 2 years. Duration = 2 years.
- Period 2: Next 2 years. Duration = 2 years.
- Period 3: Beyond 4 years up to 10 years. Duration = Total years - (Duration of Period 1 + Duration of Period 2) = 10 - (2 + 2) = 10 - 4 = 6 years.
The formula for simple interest (SI) is:
\( \text{SI} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} \)
Let's calculate the simple interest for each period using the principal amount of Rs. 5,000.
Simple Interest for Period 1 (First 2 Years)
Principal (P) = Rs. 5,000
Rate (R1) = 6% per annum
Time (T1) = 2 years
Simple Interest 1 (SI1) = \( \frac{5000 \times 6 \times 2}{100} \)
SI1 = \( \frac{60000}{100} \)
SI1 = Rs. 600
Simple Interest for Period 2 (Next 2 Years)
Principal (P) = Rs. 5,000
Rate (R2) = 8% per annum
Time (T2) = 2 years
Simple Interest 2 (SI2) = \( \frac{5000 \times 8 \times 2}{100} \)
SI2 = \( \frac{80000}{100} \)
SI2 = Rs. 800
Simple Interest for Period 3 (Remaining 6 Years)
Principal (P) = Rs. 5,000
Rate (R3) = 10% per annum
Time (T3) = 6 years
Simple Interest 3 (SI3) = \( \frac{5000 \times 10 \times 6}{100} \)
SI3 = \( \frac{300000}{100} \)
SI3 = Rs. 3,000
Total Simple Interest Earned
The total simple interest earned over 10 years is the sum of the interests from all three periods:
Total SI = SI1 + SI2 + SI3
Total SI = 600 + 800 + 3000
Total SI = Rs. 4,400
Thus, Anil will earn a total simple interest of Rs. 4,400 at the end of 10 years.
| Period | Years | Rate (%) | Principal (Rs.) | Simple Interest Calculation | Simple Interest (Rs.) |
|---|---|---|---|---|---|
| 1 | 2 | 6 | 5000 | \( \frac{5000 \times 6 \times 2}{100} \) | 600 |
| 2 | 2 | 8 | 5000 | \( \frac{5000 \times 8 \times 2}{100} \) | 800 |
| 3 | 6 | 10 | 5000 | \( \frac{5000 \times 10 \times 6}{100} \) | 3000 |
| Total Simple Interest | 4400 | ||||
Revision Table: Simple Interest Concepts
| Concept | Description | Formula |
|---|---|---|
| Principal | The initial amount of money invested or borrowed. | P |
| Simple Interest (SI) | Interest calculated only on the principal amount. | \( \text{SI} = \frac{P \times R \times T}{100} \) |
| Rate of Interest | The percentage at which interest is calculated per unit of time (usually per year). | R |
| Time | The duration for which the money is invested or borrowed. | T (in years, if rate is per annum) |
| Amount | The total sum after adding interest to the principal. | Amount = P + SI |
Additional Information: Simple vs. Compound Interest
It's important to understand the difference between simple interest and compound interest, although this problem specifically uses simple interest.
- Simple Interest: As seen in this problem, simple interest is calculated only on the initial principal amount. The interest earned does not get added back to the principal for future interest calculations. This means the principal remains constant throughout the investment period when calculating simple 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 the principal grows over time, and interest is earned on both the original principal and the accumulated interest. This typically results in much higher earnings over longer periods compared to simple interest.
In this problem, because it specifies "simple interest", we calculate the interest for each period independently based on the initial principal of Rs. 5,000, even though the rate changes.
Important Questions from Simple Interest
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?
A sum of money at simple interest amounts to Rs. 6,000 in 4 years and to Rs. 6,750 in 7 years at the same rate per cent p.a. of interest. The sum (in Rs.) is:
