Question 920740: Find the doubling time for an investment into an account bearing 8.6% interest, compounded monthly.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = p * (1+i)^n
f is the future value
p is the present value
i is interest rate per time period
n is the number of time periods.
in this problem:
set f = 2 and p = 1
this means that the future value will be double the present value.
set i = 8.6 / 100 / 12 = .086 / 12 = .07166666...
add 1 to that to get 1.0716666...
best to store it in your calculator so you can work with the full number stored there until you're done, at which time you can round as required.
n is what you are trying to solve for.
your equation becomes:
2 = 1 * (1.0716666...)^n
simplify to get:
2 = (1.0716666...)^n
take the log of both sides of this equation to get:
log(2) = log((1.0716666...)^n)
since log((1.0716666...)^n) = n * log(1.0716666...), your equation becomes:
log(2) = n * log(1.0716666...)
divide both sides of this equation by log (1.0716666...) to get:
log(2) / log(1.0716666...) = n
solve for n to get:
n = 97.06437234
your money will double in 97.06437234 months.
divide that by 12 to make it equivalent to 8.088697695 years
round as you require.
|
|
|
