Chapter 6.6, Problem 17IP

To determine

To find: Total amount in each account if interest is compounded annually.

Answer to Problem 17IP

Total amount $=A=\$4264.86$

Explanation of Solution

Given information:

Principal amount $=\$3850$

Time $=2$ years.

Interest rate $=5.25\%=0.0525$

Concept:

  $A=p{\left(1+\frac{r}{n}\right)}^{nt}$

Where

  $A=$ Total amount

  $p=$ Principal amount

  $t=$ time in years.

  $r=$ Annual interest rate.

  $n=1$ for compounded annually.

Calculation:

From given information

Principal amount $=p=\$3850$

Time $=2$ years.

Interest rate $=r=0.0525$

On substituting values in above mentioned concept

We get

  $\begin{array}{l}A=p{\left(1+\frac{r}{n}\right)}^{nt}\\ \Rightarrow A=3850{\left(1+\frac{0.0525}{1}\right)}^{2\left(1\right)}\\ \Rightarrow A=3850{\left(1+0.0525\right)}^2\\ \Rightarrow A=3850{\left(1.0525\right)}^2\\ \Rightarrow A=3850\left(1.10775625\right)\\ \Rightarrow A=\$4624.86156\end{array}$

Therefore,

To nearest cent, Total amount $=A=\$4264.86$