A sum of money invested at simple interest amounts to ₹21,500 in 5 years and ₹26,000 in 8 years. Find the principal amount (in ₹).
14,000
To find the principal amount when a sum of money is invested at simple interest, we first need to understand how simple interest works.
The formula for simple interest is:
\(SI = \frac{P \times R \times T}{100}\)
where \(SI\) is the simple interest, \(P\) is the principal, \(R\) is the rate of interest per annum, and \(T\) is the time in years.
The amount \(A\) received at the end of the period is given by:
\(A = P + SI\)
Given two scenarios:
- The sum amounts to ₹21,500 in 5 years.
- The sum amounts to ₹26,000 in 8 years.
We need to find \(P\), the principal amount.
Now, calculate the simple interest for 3 years as the difference (8 years - 5 years):
The difference in amounts = ₹26,000 - ₹21,500 = ₹4,500
This difference is the simple interest for 3 years.
So, \(SI = \frac{P \times R \times 3}{100} = ₹4,500\)
Further simplifying, we will find the interest for 1 year:
Interest for 1 year = ₹4,500 / 3 = ₹1,500
Now, compute the total interest for 5 years:
Total interest for 5 years = ₹1,500 × 5 = ₹7,500
Therefore, the principal \(P\) can be determined by:
Principal \(P = A - SI = ₹21,500 - ₹7,500 = ₹14,000\)
Thus, the principal amount is ₹14,000. Hence, the correct answer is ₹14,000.
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?
