# Bank Compounding

• Jan 27th 2007, 08:38 AM
fw_mathis
Bank Compounding
I can't seem to get these problems solved. I have attempted to follow examples given, but I continue to get stuck at a certain point in the process. Please can someone help? Thanks kindly.:confused:

Bank Account

If a bank compounds continuous, then the formula becomes simpler, that is A=P e^(rt) 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 $25,000 with the bank compounding continuously. Using 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 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place. • Jan 27th 2007, 09:18 AM CaptainBlack Quote: Originally Posted by fw_mathis I can't seem to get these problems solved. I have attempted to follow examples given, but I continue to get stuck at a certain point in the process. Please can someone help? Thanks kindly.:confused: Bank Account If a bank compounds continuous, then the formula becomes simpler, that is A=P e^(rt) 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$25,000 with the bank compounding continuously. Using 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 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.

By the look of this you have missed some data out.

RonL
• Jan 27th 2007, 09:49 AM
Soroban
Hello, fw_mathis!

You left out most of the problem . . .

Quote:

If a bank compounds continuously, the formula becomes simpler.
That is: . $A \:=\:Pe^{rt}$ where $e$ is a constant,
. . $r$ is the annual interest rate and $t$ is the number of years.

Calculate $A$ with continuous compounding.

I assume this is the last half of your previous post.
Then: . $P = 20,\!000,\;r = 0.08,\;t = 3$ . . . right?

We have: . $A \;=\;20,\!000e^{(0.08)(3)}\;\approx\;\boxed{\25,\ !424.98}$

Quote:

Now suppose, instead of knowing $t$, we know that the bank
Using logarithms, find how long we left the money in the bank (find $t$).

The equation becomes: . $25,\!000 \:=\:20,\!000e^{0.8t}\quad\Rightarrow\quad e^{0.08t}\:=\:1.25$

Take logs: . $\ln\left(e^{0.08t}\right) \:=\:\ln(1.25)\quad\Rightarrow\quad 0.08t\ln(e) \:=\:\ln(1.25)$

Therefore: . $0.08t\:=\:\ln(1.25)\quad\Rightarrow\quad t \:=\:\frac{\ln(1.25)}{0.08}\:\approx\:\boxed{2.79\ text{ years}}$

Quote:

A commonly asked question is, "How long will it take to double my money?"
At 8% interest rate and continuous compounding, what is the answer?
We want our $\20,\!000$ to grow to $\40,\!000.$
The equation is: . $40,\!000 \:=\:20,\!000e^{0.08t}\quad\Rightarrow\quad e^{0.08t} \:=\:2$
Take logs: . $\ln\left(e^{0.08t}\right) \:=\:\ln 2\quad\Rightarrow\quad 0.08t\ln(e)\:=\:\ln 2$
Therefore: . $0.08t\:=\:\ln 2\quad\Rightarrow\quad t\:=\:\frac{\ln 2}{0.08}\:\approx\:8.66\text{ years}$