SOLUTION: Help me, please? I know the formula is P=Poe^kt, but I don't how to isolate the variable to find Po?! Consider a particular investment bond that pays out 3% annual interest compo

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Question 961552: Help me, please? I know the formula is P=Poe^kt, but I don't how to isolate the variable to find Po?!
Consider a particular investment bond that pays out 3% annual interest
compounded continually. If the bond is valued at $10,000 after 10 years,
how much was it worth at 5 years?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
P=pe^(kt), using small p to avoid using subscripts. Big P is for balance of the bond after any time t. The formula rendered is . Your goal is in part, to isolate p, which you can do multiplying both sides by .

If p=1, the in 1 year, t=1, , , reasonably near the expected 3% increase. The value of constant k is the same as the interest rate of 3% or 0.03=r=k.

Your description of P=10000 after t=10 means you still want to know the initial investment amount.
-
ln(P)=ln(p)+ln(e^(kt))
ln(P)=ln(p)+kt*1
ln(P)-kt=ln(p)
-
those steps seem unnecessary although correct.


BETTER-----------------------------------------

-----you could use a calculator for this.


, the initial investment amount.

Just 5 years instead of 10 years?
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

Help me, please? I know the formula is P=Poe^kt, but I don't how to isolate the variable to find Po?!
Consider a particular investment bond that pays out 3% annual interest
compounded continually. If the bond is valued at $10,000 after 10 years,
how much was it worth at 5 years?
, with: 

 being the accumulated amount after 10 years, or the future value in 10 years

 being the accumulated amount after 5 years

 being the annual interest

 being the time, in years



We then get:

 







Accumulated amount after 5 years, or  

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