Question 1135947: How long does it take an investment of R10 000 to double if it is invested at 8% p.a. compounded annually?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the investment is doubled, then it will be equal to 20,000.
formula is 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.
the time periods are in years.
f = 20,000
p = 10,000
r = 8% / 100 = .08
formula becomes 20,000 = 10,000 * (1 + .08) ^ n
simplify to get 20,000 = 10,000 * 1.08 ^ n
divide both sides of this equation by 10,000 to get 20,000 / 10,000 = 1.08 ^ n.
simplify to get 2 = 1.08 ^ n.
take the log of both sides of this equation to get log(2) = log(1.08 ^ n)
since since log(1.08 ^ n) = n * log(1.08), the equation becomes:
log(2) = n * log(1.08).
divide both sides of this equation by log(1.08) to get:
log(2) / log(1.08) = n
solve for n to get n = 9.006468342
10,000 * 1.08 ^ 9.006468342 = 20,000, confirming the solution is correct.
your solution is that the investment will double in 9.006468342 years.
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