Solve the problem.
-Assume that a savings account earns interest at the rate of 2% compounded monthly. If this account contains $1000 now, how many months will it take for this amount to double if no withdrawals are made?
A) 417 months
B) 12 months
C) 408 months
D) 450 months

Question

Quizplus · Accepted Answer

The amount of money in the account after t months is given by the formula A = 1000(1 + 0.02/12)^12t. We want to find t such that A = 2000. Substituting this into the formula, we get 2000 = 1000(1 + 0.02/12)^12t. Dividing both sides by 1000, we get 2 = (1 + 0.02/12)^12t. Taking the logarithm of both sides, we get log(2) = 12t * log(1 + 0.02/12). Dividing both sides by 12 * log(1 + 0.02/12), we get t = log(2) / (12 * log(1 + 0.02/12)) ≈ 417. Therefore, it will take approximately 417 months for the amount in the account to double.

Solve the Problem. -Assume That a Savings Account Earns Interest at the Rate