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
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
Nirav and Mehul borrowed Rs.4000 and Rs.5000 respectively for 2.5 years at the rate of x% per annum. Mehul paid Rs 125 more interest than Nirav. Find x.
If the interest on a sum of Rs.1200 is more than the interest on Rs.1000 by Rs.120 in three years, then what is the rate of interest per annum?.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates?
A sum of Rs.1200 becomes Rs.1560 at a rate of simple interest in 3 years. In how many years will the sum of Rs.800 amount to Rs.1120 at the same rate of simple interest?
