Calculate Simple Interest Rate for Money Growth
The question asks for the annual simple interest rate (R) required for an initial sum of money to become 5 times its original value in 18 years.
Problem Analysis
- Let the principal amount be P.
- The final amount (A) is 5 times the principal: A = 5P.
- The total simple interest (SI) earned is the difference between the final amount and the principal: SI = A - P = 5P - P = 4P.
- The time period (T) is 18 years.
- We need to find the rate (R) in percent per year.
Simple Interest Formula
The formula for simple interest is:
$ SI = \frac{P \times R \times T}{100} $
Calculation Steps
- Substitute the known values into the simple interest formula:
$ 4P = \frac{P \times R \times 18}{100} $
- Cancel the principal amount (P) from both sides of the equation:
$ 4 = \frac{R \times 18}{100} $
- Rearrange the equation to solve for R:
$ R = \frac{4 \times 100}{18} $
- Calculate the value of R:
$ R = \frac{400}{18} $
$ R \approx 22.2222... $
- Round the rate to two decimal places as required:
$ R = 22.22\% $
Therefore, the annual simple interest rate required is 22.22%.
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?
