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Dec 22nd 2006, 05:59 PM
aaasssaaa

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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?
Dec 23rd 2006, 02:28 AM
CaptainBlack

Quote:

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?

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
Dec 23rd 2006, 02:34 AM
CaptainBlack

Quote:

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?

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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