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 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 \( r \)?
Show 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.
Updated On: Sep 30, 2025
- 0.41
- 0.50
- 0.75
- 1.00
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
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: \[ \boxed{0.50} \]
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: \[ \boxed{0.50} \]
Was this answer helpful?
0
0
Top GRE Quantitative Aptitude Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions
Top GRE Number System Questions
- How many integers from 3 to 30, inclusive, are odd?
- The greatest prime factor of 144 is \( x \)
The greatest prime factor of 96 is \( y \) - Dharik lives in a house on a straight street. For years, there have been 16 houses on his street to the right of his house and 17 houses on his street to the left of his house. Last year, 5 new houses were built on the same street even further to the left of those houses to the left of Dharik’s house. If these are the only houses on this street, how many houses are on this street?
- Let \( p = 4 \times 6 \times 11 \times n \), where \( n \) is a positive integer. Compare the following:
Quantity A: Remainder when \( p \) is divided by 5
Quantity B: Remainder when \( p \) is divided by 33 - How many five-digit numbers can be formed using the digits 0, 2, 3, 4 and 5, when repetition is allowed, such that the number formed is divisible by 2 or 5 or both?
View More Questions
Top GRE Questions
One pen costs \(\$\)0.25 and one marker costs \(\$\)0.35. At those prices, what is the total cost of 18 pens and 100 markers?
- Working alone at its constant rate, machine A produces kkk liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces kkk liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce kkk liters of the chemical?
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
- At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008? Give your answer to the nearest 0.1%.
- If the ratio of A to B is 3:4 and the ratio of B to C is 5:6, what is the ratio of A to C?
View More Questions