Chapter 6.6, Problem 28IP

To determine

To find: Total amount in each account if interest is compounded twice a year.

Answer to Problem 28IP

Total amount $=A=\$5540.46$

Explanation of Solution

Given information:

Principal amount $=\$3750$

Time $=2$ year.

Interest rate $=10.25\%=0.1025$

Compounded twice a year.

It means

  $n=2$

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.

  $n=2$ for compounded twice a year.

Calculation:

From given information

Principal amount $=p=\$3750$

Time $=2$ year.

Interest rate $=r=0.1025$

On substituting values in above mentioned concept

We get

  $\begin{array}{l}A=p{\left(1+\frac{r}{n}\right)}^{nt}\\ \Rightarrow A=3750{\left(1+\frac{0.1025}{1}\right)}^{2\left(2\right)}\\ \Rightarrow A=3750{\left(1+0.1025\right)}^4\\ \Rightarrow A=3750{\left(1.1025\right)}^4\\ \Rightarrow A=3750\left(1.47745544\right)\\ \Rightarrow A=\$5540.4579\end{array}$

Therefore,

To nearest cent, Total amount $=A=\$5540.46$