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
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?
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?
