Question

In what time at simple interest will a sum of money triple itself at 10 %?

• A. 10 years
• B. 20 years
• C. 15 years
• D. 5 years

Hint:

For simple interest problems, use the formula \( A = P + \frac{P \cdot r \cdot t}{100} \) and solve for the time \( t \).

Answer 1

The Correct Option is B

To determine in what time a sum of money will triple itself at a simple interest rate of 10%, we start with the formula for simple interest (SI), which is:

\(SI = \frac{P \cdot R \cdot T}{100}\)

where \(P\) is the principal amount, \(R\) is the rate of interest per annum, and \(T\) is the time in years. Here, the final amount is triple the principal, so we have:

\(3P = P + SI\)

This implies:

\(SI = 3P - P = 2P\)

Substitute \(SI = 2P\) and \(R = 10\%\) into the simple interest formula:

\(2P = \frac{P \cdot 10 \cdot T}{100}\)

Cancel \(P\) from both sides (assuming \(P \neq 0\)):

\(2 = \frac{10 \cdot T}{100}\)

Simplify and solve for \(T\):

\(2 = 0.1T\)
\(T = 20\)

Therefore, it will take 20 years for the money to triple itself at a simple interest rate of 10%.