Solve the problem.
-$8791 is deposited into a savings account at 8% interest, compounded annually. To the nearest year, how long will it take for the account balance to reach $1,000,000?

Question

Quizplus · Accepted Answer

To find the number of years it will take for the initial deposit to grow to $1,000,000, we can use the formula for compound interest: $A = P(1 + r)^t$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years.Rearranging the formula to solve for $t$, we get:$$t = \frac{\log(A/P)}{\log(1 + r)}$$Plugging in the values from the problem:$$A = 1,000,000, P = 8791, r = 0.08$$$$t = \frac{\log(1,000,000/8791)}{\log(1 + 0.08)}$$$$t = \frac{\log(113.74)}{\log(1.08)}$$$$t \approx 61.7$$Rounding to the nearest year, it will take approximately 62 years for the account balance to reach $1,000,000.

Solve the Problem. -$8791 Is Deposited into a Savings Account at 8% Interest