SOLUTION: Kyle Invests in an account earning 4.75% interest compounded continuously. How long will it take to double his investment?

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Question 1198964: Kyle Invests in an account earning 4.75% interest compounded continuously. How long will it take to double his investment?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The continuous compounding interest formula from Financial Mathematics is given as follows:

A=Pe%5E%28rt%29
r=4.75% =0.0475
to double his investment: A=2P
2P=Pe%5E%280.0475t%29.........simplify
2=e%5E%280.0475t%29........take natural logarithm of both sides
ln%282%29=ln%28e%5E%280.0475t%29%29
ln%282%29=%280.0475t%29ln%28e%29
0.0475t=ln%282%29%2Fln%28e%29..........ln%28e%29=1
0.0475t=ln%282%29
t=ln%282%29%2F0.0475
t=14.6
Answer: Kyle will double his investment in 14.6 years.