You deposit $200 in an account that doubles in 10 years. How many years will it take the account to be reduced to its original value if it loses 25 percent per year?
A) 2.00 years
B) 2.41 years
C) 3.11 years
D) 4.00 years

Question

Quizplus · Accepted Answer

The account loses 25% of its value each year, which means it retains 75% (or 0.75) of its value each year. To find the number of years $n$ it takes for the account to be reduced to its original value, we can set up the equation $200 \times 0.75^n = 100$, since the account doubles to $400 in 10 years and we want it to return to $200. Solving for $n$, we get $n = \log_{0.75}(0.5) \approx 2.41$ years.

You Deposit $200 in an Account That Doubles in 10