Using the compound interest formula, calculate the total amount at the end of the stated period.

1 answer:

6 0

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\qquad 
\begin{cases}
A=\textit{compounded amount}\\
P=\textit{original amount deposited}\to &\$5000\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, meaning once}
\end{array}\to &1\\

t=years\to &3
\end{cases}$

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Aiden wrote a riddle: Five less than 1/5 times a number is the same as the sume of the number and 1/3. Find the number.

Brrunno [24]

The number is -6.67

<em><u>Solution:</u></em>

Let "n" be the number

From given,

$\text{ Five less than 1/5 times a number } = \frac{1}{5}n - 5 = \frac{5}{n} - 5$

$\text{Sum of number and 1/3 } = n + \frac{1}{3} =\frac{3n+1}{3}$

Given that,

Five less than 1/5 times a number is the same as the sum of the number and 1/3

Therefore, we get,

$\frac{n}{5} - 5 = n + \frac{1}{3}\\\\Simplify\ the\ expression\\\\n - 25 = 5(n + \frac{1}{3})\\\\n - 25 = 5n + \frac{5}{3}\\\\n - 25 = \frac{15n + 5}{3}\\\\3n - 75 = 15n + 5\\\\12n = -80\\\\n = -6.67$