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sasogeek

  • 3 years ago

if a principal, P, is invested at r% interest compounded annually then its future value, S, after n years is given by \(\large S=P(1+ \frac{r}{100})^n \) Use this formula to show that if an interest rate of r% is compounded k times a year, then after t years \(\large S=P(1+ \frac{r}{100k})^kt \)

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  1. sasogeek
    • 3 years ago
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    Use this formula to show that if an interest rate of r% is compounded k times a year, then after t years \(\large S=P(1+\frac{r}{100k})^{kt} \)

  2. sasogeek
    • 3 years ago
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    i made a mistake with the "t" in the initial question, corrected above :)

  3. across
    • 3 years ago
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    In the formula\[S=P\left(1+\frac{r}{100k}\right)^{kt},\]"compounded anually" translates to \(k=1\), and if you let \(n=t\), then you are left with\[S=P\left(1+\frac{r}{100}\right)^n.\]

  4. across
    • 3 years ago
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    That's a hint, by the way.

  5. sasogeek
    • 3 years ago
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    yeah i noticed :) thanks x

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