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.

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) (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.
--------
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) (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:

where e is the base of the natural logarithms defined by:

If then

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

then

Taking the natural log of both sides:

Applying the rules of logarithms:

But because so

Rearranging:

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