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How do you figure out Interest Rate?

How can I figure interest rate when it is compounded daily?

  • I know that the formula for finding interest is: A=P(1+r/n)^nt But I'm having trouble with a problem that wants me to find the interest rate when I have the Current Value, the Original Value, and the time. The time is five years, compounding daily. How would I set up an equation to solve this?

  • Answer:

    Let's back up just a bit. When the interest rate compounds monthly, what you do is divide the annual interest rate by 12 and multiply the number of years by twelve to get the number of periods. So, for example, if the annual interest rate is 6% and you want to get the future value of $1,000 two years from now, you calculate $1,000(1 + 0.005)^24, rather than $1,000(1 - 0.06)^2 The same principle, although not the same numbers apply with daily compounding. If the annual interest rate is 7.3%, you use a daily interest rate of 0.02% (7.3% / 365) and you multiply the number of years by 365 to get the number of periods (you could make a distinction for leap years, but, in practice, it isn't done). So, to get the future value of $1,000 today two years from now, you calculate $1,000(1.0002)^730, instead of $1,000(1.073)^2 for annual compounding.

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I would set this up in a spreadsheet. You know what the original value is, and how many days the interest has accrued for. So if you calculate the capital times the interest for 1/365 and add that to the capital you then have the figure on which you calculate the interest for day two. Fix the interest rate in a cell at the top so that you can copy the lines down to give you 365 lines and start with a best guess at the interest rate, let's say you use 5%. Compare the total this produces with your target current value and if it is too high reduce the interest rate, or of course if your total is too low just up the interest rate. With a little trial and error you should be able fairly quickly to get the rate that gives you the correct total. Sorry I can't give you a quick formula for this, but its been a long day in which I have driven over 200 miles, and not one of those were on a Motorway or Highway.

Ian

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