Question

suppose $2800 is invested at a rate of 2.7%, compounded annually. assuming that no withdrawals are made, find the total amount after 3 years. do not round any intermediate computations, and round your answer to the nearest cent.

Explanation:

Step1: Recall compound interest formula

The compound interest formula 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, $P = 2000$, $r = 2.7\% = 0.027$, $n = 1$ (compounded annually), and $t = 3$.

Step2: Substitute values into formula

Substitute the values into the formula:
$A = 2000(1 + \frac{0.027}{1})^{1\times3}$

Step3: Simplify the expression

First, calculate the value inside the parentheses: $1 + 0.027 = 1.027$.
Then, raise it to the power of $3$: $1.027^3 \approx 1.027\times1.027\times1.027$.
Calculate $1.027\times1.027 = 1.054729$, then $1.054729\times1.027 \approx 1.083206683$.
Now, multiply by the principal: $A = 2000\times1.083206683 \approx 2166.413366$.

Step4: Round to nearest cent

Rounding $2166.413366$ to the nearest cent gives $2166.41$.

Answer:

$\$2166.41$