SOLUTION: A man makes a deposit of $50,000 into an account that pays an annual interest of 5%. How much money will be in the account after 10 years if: I. The interest is compounded continu

Question 1209277: A man makes a deposit of $50,000 into an account that pays an annual interest of 5%. How much money will be in the account after 10 years if:
I. The interest is compounded continuously
II. How long will it take for the money to triple itself if interest is compounded continuously?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Part I

P = 50000 = deposit amount
e = special constant 2.718 approximately
r = 0.05 = decimal form of the interest rate
t = 10 years

A = P*e^(r*t)
A = 50000*e^(0.05*10)
A = 82436.06353501
A = 82436.06

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Part II

The man deposits P dollars and wants it to triple to 3P dollars.
You could use P = 50,000 from earlier, but this also works for any positive real number.

The r value is the same as before.
The goal is to solve for variable t.

A = P*e^(r*t)
3P = P*e^(0.05*t)
3 = e^(0.05*t)
Ln(3) = Ln( e^(0.05*t) )
Ln(3) = 0.05*t*Ln( e )
Ln(3) = 0.05*t*1
Ln(3) = 0.05*t
t = Ln(3)/0.05
t = 21.972246

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Answers:
I. $82,436.06
II. 21.972246 years approximately

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