Need help!
At what interest rate, to the nearest hundredth of a percent, will $16,000 grow to $20,000 if invested for 5.25 years and interest rate compounded quarterly?
IIRC
$\displaystyle C = P(1+\frac{p}{n})^n$
Where,
C is the compounded amount
P is the principle (starting) amount
p is the rate (what you're after)
n is time.
Given that it is done quarterly for 5.25 years,
$\displaystyle n= (5.25)(4)$
$\displaystyle n= 21$
$\displaystyle C = 20,000$
$\displaystyle P = 16,000$
Let's do some algebra with our n value as 21.
Original Equation
$\displaystyle C = P(1+\frac{p}{21})^{(21)}$
Multiply out by P
$\displaystyle \frac{C}{P} = (1+\frac{p}{21})^{(21)}$
Take the 21st root of both sides.
$\displaystyle \sqrt[21]{\frac{C}{P}} = 1+\frac{p}{21}$
multiply both sides by 21, then subtract 21
$\displaystyle p = 21\left ( \sqrt[21]{\frac{C}{P}} \right )-21 $
Plug in the values
$\displaystyle p = 21\left ( \sqrt[21]{\frac{20,000}{16,000}} \right )-21 $
That should find you your rate.
x = 21((1.25)^(1/21)) -21 - Wolfram|Alpha
p = 22.43%
Sorry, I got the equation wrong.
This is the correct one:
$\displaystyle C = P\left ( 1 + \frac{p}{n} \right )^{nt}$
C is the compounded amount
P is the principle (starting) amount
p is the rate (what you're after)
n is times compounded annually.
t is the number of years.
Doing the same sort of stuff..
$\displaystyle (20,000) = (16,000)\left ( 1 + \frac{p}{4} \right )^{21}$
$\displaystyle \sqrt[21]{\frac{20,000}{16,000}} = 1 + \frac{p}{4}$
$\displaystyle p = (4)\sqrt[21]{\frac{20,000}{16,000}}-(4)$
p = 0.0427302 or 4.3%
x = 4((1.25)^(1/21)) -4 - Wolfram|Alpha