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
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.
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?
P borrowed an amount from Q at a simple interest of 10% p.a. At the end of the year, P paid back Rs 99000 which was 90% of what she owed. How much money did P borrow?
An amount becomes Rs. 3795 in 3 years and Rs. 4537.50 in \(7 \frac{1}{2}\) years on simple interest. Find the rate of interest per annum.
