(Advanced analysis) Susie has $500 invested in a ﬁnancial asset earning an annually compounded interest rate of 8 percent. If Susie plans to cash in the asset when it is worth $700, about how long
Will she have to wait?

Question

Quizplus · Accepted Answer

The time it takes for an investment to grow can be calculated using 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 question ($A = 700$, $P = 500$, $r = 0.08$), we can solve for $t$. This calculation gives a result close to 4.4 years, making option A the correct choice.

(Advanced Analysis) Susie Has $500 Invested in a ﬁNancial Asset