QuestionHow long will it take for a $\$ 5000$ investment to grow to $\$ 6455$ at an annual rate of $9.4 \%$, compounded quarterly? Assume that no withdrawals are made. Do not round any intermediate computations, and round your answer to the nearest hundredth.

Studdy Solution
Calculate the value of $t$ using a calculator:
$$t = \frac{\ln(1.291)}{4 \cdot \ln(1.0235)}$$ $$t \approx \frac{0.2553}{4 \times 0.0232}$$ $$t \approx \frac{0.2553}{0.0928}$$ $$t \approx 2.75$$
Round the answer to the nearest hundredth:
The time it will take for the investment to grow to \$6455 is approximately \( \boxed{2.75} \) years.