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

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Answer

Final Answer: $9.25$

Steps

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

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: $4335 = 3000 (1 + \frac{0.04}{4})^{4 t}$

Step 4 ：Solve for $t$ using algebraic methods

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

Step 6 ：Final Answer: $9.25$