Chapter 7.7, Problem 6GP

To determine

The amount of an investment.

Answer to Problem 6GP

The amount is $647.21.

Explanation of Solution

Given information:The principal amount is $300, rate of compound interest is 3.5% compounded monthly, number of year = 22.

Formula used: The compound interest formula is $A=P{(1+\frac{r}{n})}^{nt}$

Where, A = Total amount including interest, P = principal amount, r =annual rate of interest, n = number of compounding periods, t = the number of years.

Calculation:

In the problem given,

P = $300, r = $3.5\%=\frac{3.5}{100}=0.035$ , n = 12, t =22years

  $\begin{array}{l}$ A=P{(1+\frac{r}{n})}^{nt}$$ \Rightarrow A=300{(1+\frac{0.035}{12})}^{12\times 22}$$ \Rightarrow A=300{(1+\text{0}\text{.0029167})}^{264}$$ \Rightarrow A=300{(1.0029167)}^{264}$\Rightarrow A=300(\text{2}\text{.1573660071210726})\\ \Rightarrow A=\text{647}\text{.209802}\\ \Rightarrow A=647.21\end{array}$

The total amount is $647.21