Claire s mom found a very good price on a large

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haleymatthews3

06.03.2023

A) $\bf ~~~~~~ \textit{compound interest earned amount} \\\\ a=p\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} a=\textit{accumulated amount}\\ p=\textit{original amount deposited}\to & \$500\\ r=rate\to 1.5\%\to \frac{1.5}{100}\to & 0.015\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to & 1\\ t=years \end{cases} \\\\\\ a=500\left(1+\frac{0.015}{1}\right)^{1\cdot t}\implies a=500(1.015)^t$ b)so, a = 800 then, thus $\bf \textit{logarithm of exponentials}\\\\ log_a\left( x^ b \right)\implies b\cdot log_a(x)\\\\ \stackrel{a}{800}=500(1.015)^t\implies \cfrac{800}{500}=1.015^t\implies \cfrac{8}{5}=1.015^t \\\\\\ log\left( \cfrac{8}{5} \right)=log(1.015^t)\implies log\left( \cfrac{8}{5} \right)=t\cdot log(1.015) \\\\\\ \cfrac{log\left( \frac{8}{5} \right)}{log(1.015)}=t\implies 31.567993958\approx t$ so, about 31 years, 6 months, 24 days and 11 and half hours.

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Claire's mom found a very good price on a large computer monitor. she paid $325 for a monitor that was only $65 more than the original price. what was the original price ?

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