SOLUTION: How long does it take a $2800 investment to double if it's invested at 8% compounded quarterly?

Question 613671: How long does it take a $2800 investment to double if it's invested at 8% compounded quarterly?
Found 2 solutions by Theo, ewatrrr:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
f = p*(1+(i/c))^y*c
f = future value
p = present value = 2800
i = 8% per year.
c = 4
y = number of years
i/c = 2% per quarter = .02
1 + i/c = 1.02
n = y*c = number of years * compounding periods per year.
your formula becomes:
f = 2800 * (1.02)^n
since you want the future value of your principal to double, then:
f = 2*2800 = 5600
your formula becomes:
5600 = 2800 * (1.02)^n
divide both sides of this equation by 2800 to get:
2 = (1.02)^n
take the log of both sides of this equation to get:
log(2) = log(1.02^n)
this becomes:
log(2) = n*log(1.02) based on properties of logarithms.
divide both sides of this equation by log(1.02) to get:
log(2) / log(1.02) = n
solve for n using the LOG function of your calculator to get:
n = 35.00278878
it take 35.00278878 quarters for your money to double.
this equates to 35.00278878/4 = 8.750697195 years.

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!

Hi,
In General
A = Accumulated Amount Double
P= principal = 2800
r= annual rate = .08
n= periods per year = 4
t= years =
long does it take a $2800 investment to double if it's invested at 8% compounded quarterly

ln2= 4tln(1.02)
ln2/4ln(1.02) = t = 8.75yrs
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