A sum of money at a fixed rate of simple interest amounts to Rs. 1,630 in 3 years and to Rs. 1,708 in 4 years. Find the sum (in Rs.).
1396
Solving the Simple Interest Problem
The problem involves a sum of money invested at a fixed simple interest rate. We are given the amounts after 3 years and 4 years, and we need to find the original principal sum.
In simple interest, the interest earned each year is constant and is calculated only on the original principal amount. This is different from compound interest, where interest is calculated on the principal plus accumulated interest.
Understanding the Given Information
- Amount after 3 years = Rs. 1,630
- Amount after 4 years = Rs. 1,708
The increase in the amount from the end of the 3rd year to the end of the 4th year is simply the simple interest earned during the 4th year. Since simple interest is constant every year, this increase is also the interest earned in any single year.
Step-by-Step Solution to Find the Sum
Calculate the Simple Interest for One Year
The difference between the amount after 4 years and the amount after 3 years gives us the simple interest earned in the 4th year.
Simple Interest for 1 year = Amount in 4 years - Amount in 3 years
Simple Interest for 1 year = Rs. \(1708 - 1630\)
Simple Interest for 1 year = Rs. \(78\)
So, the simple interest earned per year is Rs. 78.
Calculate the Total Simple Interest for 3 Years
Since the simple interest per year is Rs. 78, the total simple interest earned over 3 years is:
Total Simple Interest for 3 years = Simple Interest for 1 year \(\times\) Number of years
Total Simple Interest for 3 years = Rs. \(78 \times 3\)
Total Simple Interest for 3 years = Rs. \(234\)
Calculate the Principal Sum
The amount after 3 years is the sum of the original principal and the total simple interest earned over 3 years.
Amount after 3 years = Principal + Total Simple Interest for 3 years
We know the Amount after 3 years is Rs. 1,630 and the Total Simple Interest for 3 years is Rs. 234. We can rearrange the formula to find the Principal:
Principal = Amount after 3 years - Total Simple Interest for 3 years
Principal = Rs. \(1630 - 234\)
Principal = Rs. \(1396\)
Therefore, the original sum (principal) is Rs. 1396.
| Item | Value (Rs.) |
|---|---|
| Amount after 3 years | 1630 |
| Amount after 4 years | 1708 |
| Simple Interest for 1 year (1708 - 1630) | 78 |
| Total Simple Interest for 3 years (78 x 3) | 234 |
| Principal (Amount after 3 years - Total Interest for 3 years) | 1630 - 234 = 1396 |
Revision Table: Simple Interest Concepts
| Term | Meaning | Formula (where P=Principal, R=Rate, T=Time) |
|---|---|---|
| Principal (P) | The initial sum of money invested or borrowed. | - |
| Interest (SI) | The extra money earned or paid. | \(SI = \frac{P \times R \times T}{100}\) |
| Rate of Interest (R) | The percentage at which interest is calculated per period (usually per year). | - |
| Time (T) | The duration for which the money is invested or borrowed. | - |
| Amount (A) | The total sum after adding interest to the principal. | \(A = P + SI\) or \(A = P + \frac{P \times R \times T}{100}\) or \(A = P(1 + \frac{R \times T}{100})\) |
Additional Information: Simple Interest vs. Compound Interest
- Simple Interest: Interest is calculated only on the original principal amount for the entire duration. The interest earned each period is constant.
- Compound Interest: Interest is calculated on the principal amount plus any accumulated interest from previous periods. The interest earned grows over time because the base on which it's calculated increases.
- This problem specifically mentions "simple interest", which is why the yearly interest is constant.
To find the rate of interest (R) in this problem, we could use the formula \(SI = \frac{P \times R \times T}{100}\). We know \(SI\) for 1 year is Rs. 78, \(P\) is Rs. 1396, and \(T\) is 1 year.
\(78 = \frac{1396 \times R \times 1}{100}\)
\(R = \frac{78 \times 100}{1396}\)
\(R \approx 5.587\%\) per annum.
However, the question only asked for the sum, which we have found to be Rs. 1396.
Similar Questions
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Important Questions from Simple Interest
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?
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?
