Question

Suppose that $2000 is invested at a rate of 3.4% compounded quarterly. Assuming that no withdrawals are made, find the total amount after 4 years. Do not round any intermediate computations and round your answer to the nearest cent.

Answer 1

Given data:

The amount invested ( principal) is

$P=\text{ \ 2,000}$

The interest rate given is

$r=3.4\%$

The number of years is

$t=4\text{ years}$

The number of times compounded is quarterly

A quarterly event happens four times a year, at intervals of three months.

$n=4$

Concept:

The formula to calculate the amount compounded is given below as

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where,} \\ A=\text{amount} \\ P=\text{principal} \\ r=\text{rate} \\ n=\text{ number of times compounded} \\ t=\text{ number of years} \end{gathered}$

By substituting the values above in the formula, we will have

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2,000(1+\frac{3.4}{400})^{4\times4} \end{gathered}$

By solving the equation above, we will have

$\begin{gathered} A=2,000(1+\frac{3.4}{400})^{4\times4} \\ A=2,000(1+0.0085)^{16} \\ A=2000(1.0085)^{16} \\ A=2,290.05 \end{gathered}$

Hence,

The final answer = $2,290.05