Question

write an exponential function to model the situation. find the amount after the specified time. $1,000 principal, 3.6% compounded monthly for 10 years

Answer 1

We can model this problem by an exponential growth:

$A=P(1+\frac{r}{n})^{nt}$

where A is the amount accumulated, P is the principal, r is the interest rate, n is the number of times per year and t is the time. By substituting our given data, we get

$\begin{gathered} A=1000(1+\frac{0.036}{12})^{12t} \\ A=1000(1+0.003)^{12t} \end{gathered}$

therefore, the model is

$A=1000(1.003)^{12t}$

Now, by substituting t=10 years, we have

$A=1000(1.003)^{120}$

then, the amount will be

$A=1432.55\text{ dollars}$