Answer:
48,856.11
Step-by-step explanation:
Compound interest is generally written as: [tex]A=P(1+\frac{r}{n})^{nt}[/tex] where P = principle amount, r = interest rate, n=compound periods, t = time. This is compounded continuously which can be defined as: [tex]A=Pe^{rt}[/tex]. If you're confused what e is, one of the definitions, is [tex]\lim_{x\to\infty}{(1+\frac{1}{x})^x[/tex]. This is essentially the very definition of continuous compound. It's when the amount of compounds (n in the equation) goes towards infinity. So using the previous defined equation simply plug the values into the equation.
[tex]A=(40000)e^{0.025*8}[/tex]
Multiply inside the exponent
[tex]A=(40000)*e^{0.2}[/tex]
raise e to the power of 0.2
[tex]A\approx40000*1.221[/tex]
Multiply
[tex]A=48,856.11[/tex]
