Chapter 6.2, Problem 57E

To determine

To find:The function that represents the balance after $t$ years.

Answer to Problem 57E

The function that represents the balance after $t$ years is $y=2000{\left(1.0125\right)}^{4t}$ .

Explanation of Solution

Given information:

Given statement is “$2000 deposit that earns $5\%$ annual interest compounded quarterly.

Formula used:

Compound interest formula is $y=P{\left(1+\frac{r}{n}\right)}^{nt}$

Where $P$ is the principal, $r$ is the annual interest rate, $t$ is times in years, and $n$ is the number of times interest is compounded per year.

From the given statement, notice that $P=2000,r=5\%=0.05,n=4$ . Substituting these values in the formula, we get,

  $\begin{array}{l}y=P{\left(1+\frac{r}{n}\right)}^{nt}\\ \Rightarrow y=2000{\left(1+\frac{0.05}{4}\right)}^{4t}\\ \Rightarrow y=2000{\left(1.0125\right)}^{4t}\end{array}$

Conclusion:

Therefore, the function that represents the balance after $t$ years is $y=2000{\left(1.0125\right)}^{4t}$ .