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Question 1144915: The doubling time of an investment is the amount of time it takes to double in value. If an investment with 4% annual compound interest is worth $8000, find its doubling time.
The doubling time is_years
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula to use if f = p * (1 + r) ^ n
f is the future value.
p is the present value.
r is the interest rate per time period.
n is the number of time periods.
to find the doubleing time, set f equal to 2 and p equal to 1.
you get 2 = 1 * (1 + r) ^ n
simplify to get:
2 = (1 + r) ^ N
when r = .04, the formula becomes:
2 = 1.04 ^ n
take the log of both sides of this equation to get:
log(2) = log(1.04 ^ n)
by logarithmic rules, this becomes:
log(2) = n * log(1.04)
divide both sides of this equation by log(1.04) to get:
log(2) / log(1.04) = n
solve for no to get:
n = 17.67298769
the investment will double ijn 17.67298769 years.
to confirm, replace n in the following equation with that number of years.
you get:
f = 8000 * 1.04 ^ 17.67298769
solve for f to get:
f = 16000.
this is double 8000, so the value for n is correct as the doubling time when the interest rate is 4% per year compounded annually.
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