You deposit $10,000 in an account that doubles in "6" years. How many years will it take the account to be reduced to its original value if it loses 10 percent per year?
A) 6.00 years
B) 6.58 years
C) 7.27 years
D) 10.00 years

Question

Quizplus · Accepted Answer

The account doubles in 6 years, so after 6 years, the balance is $20,000. To find how long it takes to reduce back to $10,000 with a 10% loss each year, we use the formula for exponential decay: $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the rate of decay (0.10 in this case), and $t$ is the time in years. Plugging in the values, we get $10,000 = 20,000(1 - 0.10)^t$. Simplifying, we find $0.5 = (0.9)^t$. Solving for $t$ gives approximately $t = 6.58$ years.

You Deposit $10,000 in an Account That Doubles in "6