Respuesta :
Interest rate of the account is 4%
Explanation:initial amount = $3313
time = 20 years
Balance = future value = $7373.22
rate = ?
n = number of times compounded
n = continuously
The formula for continuous compounding:
[tex]P=P_0e^{rt}[/tex][tex]\begin{gathered} P\text{ = amount after a certain time }=\text{ \$7373.22} \\ P_0\text{ = \$3313, t = 20 , r = ?} \\ \text{Substitute in the formula:} \\ \text{7373.22 = 3313e}^{r\times20} \\ \text{7373.22 = 3313e}^{20r} \\ \\ \text{divide both sides by 3313:} \\ \frac{\text{7373.22}}{3313}\text{ = }\frac{\text{3313e}^{20r}}{3313} \end{gathered}[/tex][tex]\begin{gathered} \frac{\text{7373.22}}{3313}\text{ = e}^{20r} \\ 2.2255\text{ = e}^{20r} \\ \text{Taking natural log of both sides:} \\ \ln \text{ 2.2255 = ln}(\text{e}^{20r}) \\ 0.8\text{ = 20r} \end{gathered}[/tex][tex]\begin{gathered} \text{divide both sides by 20:} \\ \frac{0.8}{20}\text{ = }\frac{20r}{20} \\ r\text{ = 0.04} \\ \\ In\text{ interest rate in percent = 0.04 }\times\text{ 100\% } \\ \text{interest rate in percent = 4\%} \end{gathered}[/tex]Interest rate of the account is 4%
