I’m working on a proposal of sorts, so accuracy is really important. IOW, it you have experience with this and know it cold, hands down, please respond. If not, and you’re guessing, at least please tell me you’re guessing.

Example:

I loan you 10 dollars and you pay me back 20 dollars in a day. (or 2…, or 3…)

What is my **annual** rate of return?

I have several I’m working on, with varying amounts of money and elapsed time, so I need the math that will help me drive the calculations/ results.

What say you, accountants?

This is a finance question, not an accounting question. If there is only one payment in each direction, take (ending value/beginning value) ^ (1/t) where t is the time period in years. In your example t=1/365 so take (20/10) ^ 365 = a value so large that my calculator errors out trying to calculate it.

The rate of return is the interest rate which makes the costs *equivalent *to the benefits, where equivalent means “equally attractive.” If the numbers were $100 now and $105 in a year, the RoR is obviously 5%.

Your example of $10 today and $20 tomorrow is clearly 100%, but not annually. To find the corresponding annual RoR, you first need to answer a question: are we compounding or not?

If we are compounding, that means that you would hand over the $20 next, to receive back (one assumes) $40, etc. If we are NOT compounding, you would hand over only the original $10 for your next day’s investment.

If you are not compounding, merely multiply your daily RoR by 365 to get your annual rate. If you *are *compounding, you need to use the exponent key on your calculator:

Annual Rate = (1+Daily Rate)^365 - 1

where ^ is old FORTRAN talk for “raised to the power”

Caution: if you apply these formulas to your unrealistic doubling-money-in-a-day example, you’ll get some pretty unbelievable results. But they work for real-life examples just fine…TRM