rita deposited $4000 into an account with 5.1% interest, compounded quarterly. assuming that no withdrawals…

rita deposited $4000 into an account with 5.1% interest, compounded quarterly. assuming that no withdrawals are made, how much will she have in the account after 3 years? do not round any intermediate computations, and round your answer to the nearest cent.

rita deposited $4000 into an account with 5.1% interest, compounded quarterly. assuming that no withdrawals are made, how much will she have in the account after 3 years? do not round any intermediate computations, and round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify compound interest formula

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount, $P$ is principal, $r$ is annual rate, $n$ is compounding periods per year, $t$ is time in years.

Step2: Assign values to variables

$P = 4000$, $r = 5.1% = 0.051$, $n = 4$ (quarterly), $t = 3$.

Step3: Calculate $\frac{r}{n}$

$\frac{0.051}{4} = 0.01275$

Step4: Calculate $nt$

$4 \times 3 = 12$

Step5: Compute $(1 + 0.01275)^{12}$

$(1.01275)^{12} \approx 1.16302$

Step6: Find total amount $A$

$A = 4000 \times 1.16302 \approx 4652.08$

Answer:

4652.08