Question

Compound Interest An investment of $5000 is deposited into an account in which interest is compounded monthly. Complete the table by filling in the amounts to which the investment grows at the indicated times or interest rates.

$r=4\%$

Short answer

Time (years)	Amount
1	5203.70
2	5415.71
3	5636.36
4	5865.99
5	6104.98
6	6353.71

Step-by-step solution

Step 1. Given.

$P=\mathrm{Principal}=5000$.

$r=\mathrm{interest}\mathrm{rate}=4\%=0.04$.

$n=$The number of times compounded in a year $=12$.

Because, interest is compounded monthly.

Step 2. To determine.

We have to complete the table by filling in the amounts to which the investment grows at the indicated times.

Step 3. Calculation.

Given:

$P=\mathrm{Principal}=5000$.

$r=\mathrm{interest}\mathrm{rate}=4\%=0.04$.

$n=$The number of times compounded in a year $=12$.

$t=$number of years.

$A\left(t\right)=$Amount after t years

Here,

$$\begin{gathered} A\left(t\right)=P{\left(1+\frac{r}{n}\right)}^{nt} \\ =5000{\left(1+\frac{0.04}{12}\right)}^{12t} \end{gathered}$$

We have to find $A\left(t\right)$ for $t=1,2,3,4,5,6$. We plug these values in $A\left(t\right)$.

$$\begin{gathered} A\left(1\right)=5000{\left(1+\frac{0.04}{12}\right)}^{12\left(1\right)} \\ =5203.7077146 \\ \approx 5203.71 \end{gathered}$$

$$\begin{gathered} A\left(2\right)=5000{\left(1+\frac{0.04}{12}\right)}^{12\left(2\right)} \\ =5415.7147958 \\ \approx 5415.71 \end{gathered}$$

$$\begin{gathered} A\left(3\right)=5000{\left(1+\frac{0.04}{12}\right)}^{12\left(3\right)} \\ =5636.35937259 \\ \approx 5636.36 \end{gathered}$$

$$\begin{gathered} A\left(4\right)=5000{\left(1+\frac{0.04}{12}\right)}^{12\left(4\right)} \\ =5865.99334988 \\ \approx 5865.99 \end{gathered}$$

$$\begin{gathered} A\left(5\right)=5000{\left(1+\frac{0.04}{12}\right)}^{12\left(5\right)} \\ =6104.98296971 \\ \approx 6104.98 \end{gathered}$$

$$\begin{gathered} A\left(6\right)=5000{\left(1+\frac{0.04}{12}\right)}^{12\left(6\right)} \\ =6353.7093954 \\ \approx 6353.71 \end{gathered}$$

Hence the table is:

Time (years)	Amount
1	5203.70
2	5415.71
3	5636.36
4	5865.99
5	6104.98
6	6353.71