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+(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+(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}`