How long will it take for a $\$ 3000$ investment to grow to $\$ 4335$ at an annual rate of $4 \%$, compounded quarterly? Assume that no withdrawals are made.
Do not round any intermediate computations, and round your answer to the nearest hundredth.
years

Answer

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Answer

Final Answer: $ \boxed{9.25} $

Steps

Step 1 ：To solve for the time it takes for an investment to grow at a compounded interest rate, we use the formula $ A = P(1 + \frac{r}{n})^{nt} $

Step 2 ：Given values: $ A = \$4335 $, $ P = \$3000 $, $ r = 4\% = 0.04 $, $ n = 4 $ (compounded quarterly)

Step 3 ：Substitute the given values into the formula: $ 4335 = 3000(1 + \frac{0.04}{4})^{4t} $

Step 4 ：Solve for $ t $ using algebraic methods

Step 5 ：After calculations, we find that $ t = 9.25 $ years

Step 6 ：Final Answer: $ \boxed{9.25} $