Couple algebra questions I need help with...second part.?

Question

This is the second part of the question.

If a bank compounds continuously, then the formula takes a simpler, that is
A=Pe^n
where e is a constant and equals approximately 2.7183.
Calculate A with continuous compounding. Round your answer to the hundredth's place.
Now suppose, instead of knowing t, we know that the bank returned to us $15,000 with the bank compounding continuously. Using natural logarithms, find how long we left the money in the bank (find t). Round your answer to the hundredth's place.
A commonly asked question is, “How long will it take to double my money?” At 10% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.

Answer 1

First, I should not that the "yield" I have been reporting is the interest earned. Add $10,000 for the total amount in the account at the end of the investment period.

Second, you wrote the formula incorrectly. The formula for continuous compounding has to include the interest rate, so
A = Pe^(rt)

Given the information from the previous question ($10,000 at 10% for 2 years), continuous compounding would yield $2,214.03.

If we know that the bank returned $15,000 on a $10,000 deposit at 10%, the length of time must have been 4.05 years.

In 6.93 years, a deposit will have doubled.

I apologize for the delay on responding to these questions--I have been on vacation.

Answer 2

your leaving alot of info out of the equation
the actual formula for continous compounding is A=Pe^rt
a is end amount
P is principal or amount put in
e is e
r is rate or percentage times 1/100
t is time
all you give for information is that 15000=Pe^rt
not knowing what any of these variables are t can only be solved for in term of P and r
t=(ln(15000/P))/r
entering the info from your previous question though gives that t=4.05
part 2
use the same formula as above A=Pe^rt
you simply add in that you want A to equal 2P
and that r=.10
thus putting in (2P=Pe^(.1t))
solving this for t gives you about 6.93
the P's cancel out

Answer 3

If we're talking about doubling your money, then

2 = e^n

or

e = ln 2

I didn't see the first part of the question, so I'm not sure what the units are. ln 2 is smaller than 1, so if the time unit is years, I want to deposit my money in that bank.