Understanding the Simple Interest Problem
The question asks us to find the factor (\(n\)) by which a sum of money grows in 20 years, given that it triples itself in 8 years at simple interest. Simple interest means the interest earned each year is constant and calculated only on the initial principal amount.
Calculating the Rate of Simple Interest
Let the principal amount be \(P\). The problem states that the sum of money triples itself in 8 years. This means the final amount (\(A\)) after 8 years is \(3P\). The formula for the final amount (\(A\)) in simple interest is \(A = P + SI\), where \(SI\) is the simple interest earned.
So, the simple interest earned in 8 years is:
\( SI = A - P = 3P - P = 2P \)
Now, we use the simple interest formula:
\( SI = \frac{P \times R \times T}{100} \)
Here, \(SI = 2P\) and \(T = 8\) years. Plugging these values in:
\( 2P = \frac{P \times R \times 8}{100} \)
We can cancel \(P\) from both sides (assuming \(P \ne 0\)):
\( 2 = \frac{R \times 8}{100} \)
Now, we solve for the rate (\(R\)):
\( R = \frac{2 \times 100}{8} \)
\( R = \frac{200}{8} \)
\( R = 25\% \)
So, the rate of simple interest is 25% per year.
Finding the Value of \(n\)
Next, we need to find out how many times (\(n\)) the principal amount becomes in 20 years at this rate (\(R = 25\%\)).
Let the final amount after 20 years be \(nP\). The simple interest earned in 20 years (\(T = 20\)) is:
\( SI = nP - P = (n-1)P \)
Using the simple interest formula again with \(R = 25\%\) and \(T = 20\):
\( SI = \frac{P \times R \times T}{100} \)
\( (n-1)P = \frac{P \times 25 \times 20}{100} \)
Cancel \(P\) from both sides:
\( n-1 = \frac{25 \times 20}{100} \)
\( n-1 = \frac{500}{100} \)
\( n-1 = 5 \)
Solving for \(n\):
\( n = 5 + 1 \)
\( n = 6 \)
Therefore, the sum of money becomes 6 times itself in 20 years.
Similar Questions
- What is the initial rate of interest per annum ?
- What is the ratio of the interest on the first loan to the interest on the second loan ?
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?
