SOLUTION: If $500 is deрosited in an ассount paying 8.5% annual interest, compounded semiannually, how long willit take for the асcount to increase to $1000? Нow long will it take for

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Question 1176171: If $500 is deрosited in an ассount paying 8.5% annual interest, compounded semiannually, how long willit take for the асcount to increase to $1000? Нow long will it take for the account to increase to $1000 if compounded continuously?

Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website!
This is the doubling time of money at 8.5%
Rule of 70 will say a little more than 8 years (70/8.5)
P=Po(1+(r/t))^nt
1000=500(1.0425)^nt
2=1.0425^nt
ln of both sides
ln 2=nt ln(1.0425)
divide both sides by ln 1.0425
nt=16.65
n=2
so t=8.325 years.
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The second is 2=e^0.085t
ln both sides
ln2=0.085 t
t=8.15 years, consistent with the rule of 70 (which is actually the rule of 69.3, which is the ln 2 multiplied by 100 to work with rates in per cent rather than decimals.)

Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website!
.

            The answer in the post by @Boreal is INCORRECT.

To get a correct answer, you MUST round the value of 8.35 years to 8.5 years (8 years and 6 months)

in order for the bank would make the last compounding.