SOLUTION: How long will it take for $8900 to grow to $31,000 at an interest rate of 11.9 % if the interest is compounded continuously? Round to nearest hundreth.

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Question 169820: How long will it take for $8900 to grow to $31,000 at an interest rate of 11.9 % if the interest is compounded continuously? Round to nearest hundreth.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How long will it take for $8900 to grow to $31,000 at an interest rate of 11.9 % if the interest is compounded continuously? Round to nearest hundreth.
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A(t) = Pe^(rt)
31000 = 8900*e^(0.119t)
e^(0.119t) = 31000/8900
Take the natural log of both sides to get:
0.119t = ln[31000/8900]
t = (1/0.119)*ln[31000/8900]
t = 10.49 years
Cheers,
Stan H.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Future Value (FV) in terms of Present Value (PV), interest rate (i), and number of years (Y) under continuous compounding is:

FV=PVe%5E%28iY%29 where e is the base of the natural logarithms defined by:

If y+=+e%5Ex then ln%28x%29+=+y

Given:
FV = 31000
PV = 8900
i = 11.9% = .119

then

31000=8900e%5E%28.119Y%29

Taking the natural log of both sides:

ln%2831000%29=ln%288900e%5E%28.119Y%29%29

Applying the rules of logarithms:

ln%2831000%29=ln%288900%29%2Bln%28e%5E%28.119Y%29%29

ln%2831000%29=ln%288900%29%2B0.119Yln%28e%29

But ln%28e%29=1 because ln%28e%5Ex%29=x so ln%28e%5E1%29=1

Rearranging:

0.119Y=ln%2831000%29+-+ln%288900%29
Y=%28ln%2831000%29-ln%288900%29%29%2F0.119

A little calculator work gets you to about 10.49 years rounded to the nearest hundreth.