Question

Write a function A that models the amount to which the account grows after T years

Answer 1

item (a):

Using the formula given in the question, we have

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

Our principal investment P is equal to $4000, our interest r is 3 1/4 %, writting this in decimal form we have

$3\frac{1}{4}=3+\frac{1}{4}=3.25$

Since it is a percentage, to write in decimal we divide by 100

$\frac{3.25}{100}=0.0325$

And finally, our n value is 365 since it is compounded daily, and we have 365 days in a year.

Then, our function is

$A(t)=4000(1+\frac{0.0325}{365})^{365t}_{}$

item (b):

To find A(30), we just need to evaluate this value in the function we created before

$A(30)=4000(1+\frac{0.0325}{365})^{365\cdot30}_{}=10604.2085587\ldots\approx10604.21$

This means that with an investment of $4000, with this rate Joe is going to have a return of $10604.21.