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
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?
