# Determine the time it takes to double an investment in an account that pays interest of 4% per annum, compounded quarterly cant figure out how to solve this...

degeneratecircle | High School Teacher | (Level 2) Associate Educator

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If the initial investment is `A`, the amount after `t` years is given by

`A(t)=A(1+.04/4)^(4t)=A(1.01)^(4t)`

The `.04` is `4%` , the division by 4 is because it's compounded 4 times per year, and the 4 in the 4t is for the same reason. Now if you want to double your amount, you want to end up with `2A` , so you should solve

`2A=A(1.01)^(4t),` which is equivalent to `2=1.01^(4t).` If you haven't learned logarithms yet, you can solve this graphically using the graph below. If you have learned logarithms, take the log of both sides of `2=1.01^(4t)` to get

`log 2=log (1.01^(4t))=4t log (1.01),` so

`t=(log 2)/(4log(1.01))~~17.4` years.

Sources:

degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted on

One thing to think about is whether the bank would say you have double at 17.4 years or make you wait until the next quarter year ends at 17.5 years. The wikipedia article uses `|__nt__|` , which means round down to the nearest integer, which means that after 17.4 years your investment would only be about 1.98 times the original and you would have to wait another tenth of a year to really double it.

But I haven't seen that elsewhere and most math books would give the answer as 17.4. I suspect it would depend on the bank. Anyway, it's a relatively minor point and doesn't significanly change the problem.