1. ## Exponential Function

Hey guys, so I have a question that goes "An investment of $1500 is earning interest at 12%, compounded quarterly (every 3 months). Write an exponential function for the amount,$\displaystyle A(t)$, of the investment after t years. Now the answer I came up with was$\displaystyle
A(t)=1500(1.12)^{4t}
$I came upon 1.12, because that would be a 12% increase on the previous amount, right? But when I went to check my answer, it seems that the correct answer is;$\displaystyle A(t)=1500(1.03)^{4t}$I have no idea why they are using 1.03, or where they even got 1.03? Can anyone shed some light on this? Thanks! 2. Originally Posted by Kasper Hey guys, so I have a question that goes "An investment of$1500 is earning interest at 12%, compounded quarterly (every 3 months). Write an exponential function for the amount, $\displaystyle A(t)$, of the investment after t years.

Now the answer I came up with was
$\displaystyle A(t)=1500(1.12)^{4t}$

I came upon 1.12, because that would be a 12% increase on the previous amount, right? But when I went to check my answer, it seems that the correct answer is;

$\displaystyle A(t)=1500(1.03)^{4t}$

I have no idea why they are using 1.03, or where they even got 1.03? Can anyone shed some light on this? Thanks!
Hi kasper,

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

Where,

A = Amount accumulated after n years with interest

P = Principal amount (initial amount)

r = Annual % rate as a decimal. In your case r = .12

n = Number of times it's compounded each year. In your case, n = 4 (quarterly)

t = Number of years

You just need to divide the rate (.12) by 4 to get .03 and then you arrive at:

$\displaystyle A(t)=1500(1.03)^{4t}$

3. Ah, that makes good sense, thanks masters