How do you calculate compounding interest if the time period is obscure.

On September 3, 2013 you invested $1,000 at the annual risk-free rate of 5% until APR. 18, 2014.
Calculate the amount you will receive if the annual 5% rate is compounded

4.1 – annually; 4.2 – quarterly; 4.3– monthly;
4.4 – daily; 4.5 – continuously.

There is 7 months and 15 days between the two dates.

Believe you should just be able to break it down and say its .xx years. I think they just generally give it as an annual rate for ease of comparison

You use x/365 instead of number of years.
So count the days. An easy way to do this is to plot both dates into excel, eg A1 and A2. If the cells are set to the date format, you can in cell A3 write =A2-A1 and it will return the amount of days inbetween. For your example there are 227 days

Then you apply your standard formula:

A = P*(1+(r/n))^nt

and for continous compounding:
A = P*e^rt

4.1:
1000*(1+ 0,05/1)^1*(227/365)

4.2:
1000*(1+ 0,05/2)^2*(227/365)

4.3
1000*(1+ 0,05/12)^12*(227/365)

4.4
1000*(1+ 0,05/365)^365*(227/365)

4.5
1000*e^(0,05*(227/365))

This post was edited by Simens on Sep 10 2013 05:29pm

simens solution looks correct to me. for brownie points you can mention in your solution that a lot of times it is r/360 rather than r/365

That's known as the banker's rule. Unless specifically stated, you do not use Banker's Rule.
Simens is correct in his answers at first glance.

thanks a lot guys

no problem

and yes, the use of 360 is generally accepted as well as long as you state why you use it. Generally in finance we say that there are either 250 or 252 trading days per year, depending who you ask