Question

felipe deposited $4000 into an account with 5.4% interest, compounded annually. assuming that no withdrawals are made, how much will he have in the account after 5 years? do not round any intermediate computations, and round your answer to the nearest cent.

Explanation:

Step1: Recall compound interest formula

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where:

• $A$ is the amount of money accumulated after $n$ years, including interest.
• $P$ is the principal amount (the initial amount of money).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times that interest is compounded per year.
• $t$ is the time the money is invested for in years.

Here, $P = 4000$, $r = 5.4\% = 0.054$, $n = 1$ (compounded annually), and $t = 5$.

Step2: Substitute values into formula

Substitute the values into the formula:
$A = 4000(1 + \frac{0.054}{1})^{1\times5}$
Simplify the exponent and the fraction:
$A = 4000(1 + 0.054)^{5}$
$A = 4000(1.054)^{5}$

Step3: Calculate $(1.054)^5$

First, calculate $1.054^5$. Let's compute step by step:
$1.054^2 = 1.054\times1.054 = 1.110916$
$1.054^3 = 1.110916\times1.054 \approx 1.170905464$
$1.054^4 = 1.170905464\times1.054 \approx 1.234134359$
$1.054^5 = 1.234134359\times1.054 \approx 1.300777614$

Step4: Calculate $A$

Now, multiply by the principal:
$A = 4000\times1.300777614 \approx 5203.11$

Answer:

$\$5203.11$