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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   



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) About Me  (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 P=pe%5E%28kt%29. Your goal is in part, to isolate p, which you can do multiplying both sides by e%5E%28-kt%29.

If p=1, the in 1 year, t=1, P=1%2Ae%5E%280.03%2A1%29, P=e%5E%280.03%29=1.0304, 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-----------------------------------------
pe%5E%28kt%29=P
p=P%2Fe%5E%28kt%29-----you could use a calculator for this.
p=10000%2F%28e%5E%280.03%2A10%29%29
p=10000%2F%28e%5E%280.3%29%29
highlight%28p=7408.18%29, the initial investment amount.

Just 5 years instead of 10 years?
P=7408.18%2Ae%5E%280.03%2A5%29
P=7408.18%2A1.1618342427
highlight%28P=8607.08%29

Answer by MathTherapy(10555) About Me  (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?
A+=+P%5Bo%5De%5E%28rt%29, with: 
A being the accumulated amount after 10 years, or the future value in 10 years
P%5Bo%5D being the accumulated amount after 5 years
r being the annual interest
t being the time, in years
We then get:
A+=+P%5Bo%5De%5E%28rt%29
10000+=+P%5Bo%5De%5E%28.03%285%29%29
10000+=+P%5Bo%5De%5E.15
P%5Bo%5D+=+10000%2Fe%5E.15
Accumulated amount after 5 years, or highlight_green%28P%5Bo%5D+=+%22%24%228607.08%29