Chapter 13.1, Problem 54E

To determine

To calculate: The account balance after each of the first three years.

Answer to Problem 54E

The account balance after first year is $\$2264.12$ after second year is $\$2395.44$ and after third year is $\$2534.38$ .

Explanation of Solution

Given information:

The initial balance is $\$2140$ in her account. Savings account of hers has an annual yield of $5.8\%$ .

Formula used:

The iterative function $p_{n+1}=p_n+r{p}_n$ where, $p_n$ is the principal amount after n periods of time and r is the rate of interest.

Calculation:

Consider the provided information that initial balance is $\$2140$ in her account. Savings account of hers has an annual yield of $5.8\%$ .

Apply the iterative function $p_{n+1}=p_n+r{p}_n$ where, $p_n$ is the principal amount after n periods of time and r is the rate of interest.

Rate of interest is,

  $\begin{array}{c}r=5.8\%\\ =\frac{5.8}{100}\\ =0.058\end{array}$

Now, $p_n=2140\text{ and }r=0.058$ .

Therefore, balance after first year is,

  $\begin{array}{c}{p}_1=2140+\left(0.058\right)\left(2140\right)\\ =2264.12\end{array}$

Now, $p_n=2264.12\text{ and }r=0.058$ .

Therefore, balance after second year is,

  $\begin{array}{c}{p}_2=2264.12+\left(0.058\right)\left(2264.12\right)\\ =2395.44\end{array}$

Now, $p_n=2395.44\text{ and }r=0.058$ .

Therefore, balance after third year is,

  $\begin{array}{c}{p}_3=2395.44+\left(0.058\right)\left(2395.44\right)\\ =2534.38\end{array}$

Thus, the account balance after first year is $\$2264.12$ after second year is $\$2395.44$ and after third year is $\$2534.38$ .