Question
were deposited into an account wit
a
interest rate, compounded
continuously. How many years was it in
the bank if the current amount is
?
Round to the nearest year.
a
continuously. How many years was it in
the bank if the current amount is
Ask by Murray Pearson. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The account was in the bank for approximately 46 years.
Solution
To solve this problem, we can use the formula for continuous compounding of interest:
where:
-
is the current amount in the account, -
is the initial deposit, -
is the interest rate, -
is the time in years.
Given:
- Initial deposit
, - Interest rate
, - Current amount
.
We need to find the time
in years.
Substitute the given values into the formula:
Now, we can solve for
using the formula:
Let’s calculate the value of
using the formula.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Divide the terms:
- step2: Rewrite the expression:
- step3: Multiply by the reciprocal:
- step4: Reorder the terms:
The timein years is approximately 46.05 years.
Therefore, the account was in the bank for approximately 46 years.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Bonus Knowledge
To find the time
for continuous compounding, you can use the formula:
where
is the amount of money accumulated after time
,
is the principal amount (the initial money),
is the rate of interest, and
is Euler’s number (approximately
).
In your case,
,
, and
. Plugging in these values, we have:
Dividing both sides by 600 gives:
Taking the natural logarithm of both sides:
Now, solve for
:
Rounding to the nearest year,
.
So, the answer is: