Calculating Simple Interest Rate
The problem asks for the annual interest rate at which a sum of money multiplies five times its original value in 11 years.
Understanding Simple Interest Concepts
Let the principal amount be P. According to the question, the final amount (A) becomes five times the principal.
- Amount, $A = 5P$
- Time period, $T = 11$ years
The Simple Interest (SI) earned is the difference between the Amount and the Principal:
$ SI = A - P $ $ SI = 5P - P $ $ SI = 4P $Applying the Simple Interest Formula
The formula for Simple Interest is:
$ SI = \frac{P \times R \times T}{100} $Where:
- P = Principal amount
- R = Rate of interest per annum (in %)
- T = Time period (in years)
Solving for the Rate (R)
Substitute the known values into the formula:
$ 4P = \frac{P \times R \times 11}{100} $We can cancel out P from both sides (assuming P is not zero):
$ 4 = \frac{R \times 11}{100} $Now, rearrange the equation to solve for R:
$ R = \frac{4 \times 100}{11} $ $ R = \frac{400}{11} $To express the rate as a mixed fraction:
$ R = 36\frac{4}{11}\% $Therefore, the sum of money will become five times itself in 11 years at an annual rate of $36\frac{4}{11}\%$.
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?
