ewaddell25
contestada

Use
A=P(1+rn)nt
A=P(1+rn)nt where:
A = the amortized amount (total loan/investment amount over the life of the loan/investment)
P = the initial amount of the loan/investment
r = the annual rate of interest
n = the number of times interest is compounded each year
t = the time in years

Find how long it takes a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly.

It will take ___ years. (Round answer to 3 decimal places.)

Respuesta :

same here, the interest earned is 210, the principal is 2200, so the accumulated amount is 2410.

[tex]\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\$2410\\ P=\textit{original amount deposited}\to &\$2200\\ r=rate\to 10\%\to \frac{10}{100}\to &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years \end{cases}[/tex]

[tex]\bf 2410=2200\left(1+\frac{0.1}{12}\right)^{12t}\implies \cfrac{2410}{2200}=\left(1+\frac{1}{120} \right)^{12t} \\\\\\ \cfrac{241}{220}=\left(\cfrac{121}{120} \right)^{12t}\implies log\left( \frac{241}{220} \right)=log\left[ \left(\frac{121}{120} \right)^{12t} \right]\\\\\\ log\left( \frac{241}{220} \right)=12t\cdot log\left(\frac{121}{120} \right)\implies \cfrac{log\left( \frac{241}{220} \right)}{12 log\left(\frac{121}{120} \right)}=t\implies 0.915 \approx t[/tex]

so, about 10 months and 27 days.

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