Respuesta :
[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$625\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &12 \end{cases} \\\\\\ A=625e^{0.07\cdot 12}\implies \implies A=625e^{0.84}\implies A\approx 1447.73[/tex]
The investment will be $1447.73 worth in 12 years.
What is continuous compound interest?
Continuous compounding exists the mathematical limit that compound interest can reach if it's calculated and reinvested into an account's balance over a theoretically infinite number of terms. While this exists not possible in practice, the vision of continuously compounded interest stands important in finance.
Since, the amount formula is compounded continuously,
[tex]$A=P e^{r t}$[/tex]
Where,
P is the principal amount,
[tex]$\mathbf{r}$[/tex] is the rate per period,
t is the number of periods,
e is Euclid number,
Here, [tex]$P=\$ 625$[/tex],
[tex]$r=7 \%=0.07 \text {, }$[/tex]
t=12 years
Thus, the amount after 12 years would be,
[tex]$A=625 e^{0.07 \times 12}=625 e^{0.84}=\$ 1447.72936049 \approx \$ 1447.73$[/tex]
Hence, $1447.73 will the investment be worth 12 years.
To learn more about continuous compound interest refer to:
https://brainly.com/question/27778743
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