If you earn 11% per year on your bank account, how long will it take an account with $110 to double to $220?

Question

I also need to know how to round the answer to two decimal places

 

Answer 1

M(t) = amount of money as a function of time t in years

 

If you earn 11% each year, then at the end of each year you will have 1.11 times the amount you had at the beginning of the year.  This repeats every year, so after t years, you will have 1.11^t times as much as you had to start with.  Then

 

M(t) = (initial amount) x (1.11^t)

 

M(t) = $110 x 1.11^t

 

To find how long it takes to double, set M(t) = $220 and solve for t.

 

$220 = $110 x 1.11^t

 

2 = 1.11^t

 

log2 = t log1.11

 

t = log2 / log1.11 ≅ 6.642 years

 

Test the solution.