Question 1114145: a) Grace invests £250,000 at a 6.5% interest rate annually. Compounding the interest annually, how long will it take his investment to double?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if he doubles his investment, then the future value is 250,000 * 2 = 500,000.
the formula to use is f = p * (1+r)^n
f is the future value.
p is the present value
r is the interest rate per year
n is the number of yers.
formula becomes 500,000 = 250,000 * (1 + .065) ^ n
divide both sides of this formula by 250,000 and you get 2 = (1 + .065) ^ n
take the log of both sides of this euation and you get log(2) = log((1 + .065) ^ n)
this is equivalent to log(2) = n * log(1 + .065)
divide both sides of this equation by log(1 + .065) and solve for n to get n = log(2) / log(1 + .065).
this makes n = 11.00673904
the money will double in 11.00673904 years.
250,000 * (1 + .065) ^ 11.00673904 = 500,000.
11.00673904 years is your answer.
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