Question

bill deposited $4000 into an account with 4.2% interest, compounded monthly. assuming that no withdrawals are made, how much will he have in the account after 6 years? do not round any intermediate computations, and round your answer to the nearest cent.

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert values to appropriate form

Given $P = 4000$, $r=0.042$ (since $4.2\%= 0.042$), $n = 12$ (compounded monthly), and $t = 6$.

Step3: Substitute values into the formula

$A=4000(1 +\frac{0.042}{12})^{12\times6}=4000(1 + 0.0035)^{72}$.

Step4: Calculate the value inside the parentheses

$1+0.0035 = 1.0035$.

Step5: Calculate the exponentiation

$(1.0035)^{72}\approx1.28397$.

Step6: Calculate the final amount

$A = 4000\times1.28397=5135.88$.

Answer:

$5135.88$