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how much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $14,000 in three years

Respuesta :

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$14000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\to &2\\ t=years\to &3 \end{cases} \\\\\\ 14000=P\left(1+\frac{0.06}{2}\right)^{2\cdot 3}\implies 14000=P(1.03)^6\implies \cfrac{14000}{1.03^6}=P[/tex]

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