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  1. #1
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    1) if an old stamp is currently worth $60. The stamp's value will grow exponential by 15% each year. When will the stamp be wroth three times its intial value?

    2) Mark invests $500 in a savings plan that pays interest, which is compounded monthly. At the end of 10 years, his intial investment is worth $909.70. What interest rate did the plan pay?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by aaasssaaa View Post
    1) if an old stamp is currently worth $60. The stamp's value will grow exponential by 15% each year. When will the stamp be wroth three times its intial value?

    If p is the principle and r the intrest rate (in %) the value after n years is:

    <br />
V=p\,(1+r/100)^n<br />

    Now for your problem you want V=3p and r=15 and solve for n:

    p\,(1.15)^n=3\,p,

    so:

    n\ \ln(1.15)=\ln(3),

    so:

    n=\frac{\ln(3)}{\ln(1.15)}\approx 7.86 \mbox{ years}

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by aaasssaaa View Post
    2) Mark invests $500 in a savings plan that pays interest, which is compounded monthly. At the end of 10 years, his intial investment is worth $909.70. What interest rate did the plan pay?
    If r is the % rate per period then you have:

    500\ (1+r/100)^{120}=909.70

    which you need to solve for r which is the interest rate per
    month.

    This is because 10 years is 120 periods.

    RonL
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