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anonymous

  • 4 years ago

Interest formula P= Principle 1000 n = number of years 3 I = rate 5% m= ending balance 1157.63 1000 * (1+i) to the 3rd power = 1157.63 1000 * (1+.05) to the 3rd power =1157.63 1000 * (1.05 * 1.05 *1.05 ) = 1157.63 How do I solve for i if everything else is known? Thank you

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  1. anonymous
    • 4 years ago
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    This was just an example. Assume I know everything else but the rate and want to determine it.

  2. ash2326
    • 4 years ago
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    We have Ending Balance = Principle*(1+Rate)^{Time in years} m=P*(1+i)^t to find i? \[\frac{m}{p}=(1+i)^t\] take log boths sides \[log_{10} \frac{m}{p}=t *log_{10}(1+i)\] \[\frac{1}{t}log_{10} \frac{m}{p}=log_{10}(1+i)\] take anti log both sides \[\large{1+i=10^{\frac{1}{t}log_{10} \frac{m}{p}}}\] or \[\large{i=10^{\frac{1}{t}log_{10} \frac{m}{p}}-1}\]

  3. ash2326
    • 4 years ago
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    or \[i=(\frac{m}{p})^{\frac{1}{t}}-1\]

  4. anonymous
    • 4 years ago
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    I think you have it, but I don't know how I would use it with the 1 over t power. I don't see how to do the math. Thanks

  5. anonymous
    • 4 years ago
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    Ah yes I should've realized it wasn't simple interest formula when he was cubing the time. lol

  6. anonymous
    • 4 years ago
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    Figured out how to use your formula with an exponential calculator, Thanks for your help. I had an Algebra teacher look at it and not be able to figure it out.

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