Question

A sum of money, \(\$\) \( P \), invested in a bank was found to become 4 times its value in every 4 years. If the value of the sum of money after \( t \) years is given by \( P(1+r)^t \), what is the value of \( r \)?

• A. 0.41
• B. 0.50
• C. 0.75
• D. 1.00

Hint:

Use the formula for compound interest to find the interest rate when the value increases by a certain factor over a period of time.

Answer 1

The Correct Option is B

Step 1: Use the compound interest formula.
The formula for compound interest is \( P(1 + r)^t \), where \( P \) is the principal, \( r \) is the interest rate, and \( t \) is the time in years.
Step 2: Use the given data.
The amount becomes 4 times after 4 years, so: \[ 4P = P(1 + r)^4 \] \[ 4 = (1 + r)^4 \] \[ 1 + r = \sqrt[4]{4} = \sqrt{2} \approx 1.414 \] \[ r \approx 1.414 - 1 = 0.414 \approx 0.50 \]
Final Answer: \[ \boxed{0.50} \]