The future value of $4000 invested for 5 years at rate r, compounded annually, is given by S =4000(1=r)⁵. Find the rate r, as a percent, that gives a future value from $5610 to $6442, inclusive. Round to the nearest whole percent. A) $7 \% \leq \mathrm { r } \leq 10 \%$ B) $7 \% \leq \mathrm { r } \leq 15 \%$ C) $8 \% \leq \mathrm { r } \leq 13 \%$ D) $6 \% \leq \mathrm { r } \leq 9 \%$

Question

Quizplus · Accepted Answer

The correct formula for future value is $S = 4000(1 + r)^5$. To find the rate $r$, we solve for $r$ when $S = 5610$ and $S = 6442$. For $S = 5610$, $5610 = 4000(1 + r)^5$ leads to $r \approx 7\%$. For $S = 6442$, $6442 = 4000(1 + r)^5$ leads to $r \approx 10\%$. Therefore, $7 \% \leq \mathrm { r } \leq 10 \%$.

The Future Value of $4000 Invested for 5 Years at Rate