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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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Originally Posted by aaasssaaa

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?

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

$\displaystyle
V=p\,(1+r/100)^n
$

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

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

so:

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

so:

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

RonL

Quote:

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Originally Posted by aaasssaaa

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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If $\displaystyle r$ is the % rate per period then you have:

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

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

This is because 10 years is 120 periods.

RonL