Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.875/100
r = 0.03875 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 10,000.00(1 + 0.03875/12)(12)(7.5)
A = 10,000.00(1 + 0.003229167)(90)
A = $13,366.37
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 3.875% per year compounded 12 times per year over 7.5 years is $13,366.37.
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$149000\\ P=\textit{original amount deposited}\dotfill & \$9800\\ r=rate\to 11.6\%\to \frac{11.6}{100}\dotfill &0.116\\ t=years \end{cases} \\\\\\ 149000=9800e^{0.116\cdot t}\implies \cfrac{149000}{9800}=e^{0.116\cdot t}\implies \cfrac{745}{49}=e^{0.116t}[/tex]
[tex]\log_e\left( \cfrac{745}{49} \right)=\log_e\left( e^{0.116t} \right)\implies \log_e\left( \cfrac{745}{49} \right)=0.116t \\\\\\ \cfrac{\ln\left( \frac{745}{49} \right)}{0.116}=t\implies 23.46\approx t[/tex]
