Chapter 7.7, Problem 26PPS

To determine

To calculate: The total amount to the nearest cent.

Answer to Problem 26PPS

The total amount is $2671.60

Explanation of Solution

Given information: The principal amount is $2500, rate of compound interest is 6.75% per annum, number of year = 1. The interest is compounded twice a year.

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 = $2500, r = $6.75\%=\frac{6.75}{100}=0.0675$ , n = 2, t =1year

  $\begin{array}{}$ A=P{(1+\frac{r}{n})}^{nt}$$ \Rightarrow A=2500{(1+\frac{0.0675}{2})}^{2\times 1}$$ \Rightarrow A=2500{(1+0.0375)}^2$$ \Rightarrow A=2500{(1.03375)}^2$$ \Rightarrow A=2500(\text{1}\text{.0686390625})$$ \Rightarrow A=\text{2671}\text{.59765625}$$ \Rightarrow A=\text{2671}\text{.60}$\end{array}$

The total amount is $2671.60