1. ## Interest, compounded quarterly..

I am unsure/unaware of the formula and how to use it to complete this problem. Any help is greatly appreciated.

Art invests $2700 in a savings account that pays 9% interest, compounded quarterly. if there are no other transactions, when will his balance reach$4550?

2. Originally Posted by Wesker
I am unsure/unaware of the formula and how to use it to complete this problem. Any help is greatly appreciated.

Art invests $2700 in a savings account that pays 9% interest, compounded quarterly. if there are no other transactions, when will his balance reach$4550?
Use this formula:
$\displaystyle P(t) = P_0\left(1 + \frac{r}{k}\right)^{kt}$, where

$\displaystyle P_0$ is the initial amount,
$\displaystyle r$ is the interest in decimal,
$\displaystyle k$ is the number of times per year the interest is compounded, and
$\displaystyle t$ is the time in years.

The equation for the above problem would then be
$\displaystyle 4550 = 2700\left(1 + \frac{0.09}{4}\right)^{4t}$,
then solve for t.

01

3. A little bit of an explanation of the formula yeongil gave: If the interest rate is r per year, then it is r/k every "kth" of a year. That is, each "kth" of a year, for principal P, we calculate (r/k)P and add it to P: P+ (r/k)P= P(1+ r/k). Every "kth of a year" we multiply by that (1+ r/k). Since there are k "kths" in a year, in t years, we will have multiplied kt times. Multiplying by the same thing kt times is the same as multiplying by $\displaystyle (1+ r/k)^{kt}$, thus yeongil's formula: $\displaystyle P(1+ r/k)^{kt}$.