Question
A person invests 7500 dollars in a bank. The bank pays
the nearest tenth of a year, how long must the person leave the money in the bank until it
reaches 14300 dollars?
the nearest tenth of a year, how long must the person leave the money in the bank until it
reaches 14300 dollars?
Ask by Clarke Tucker. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The person needs to leave the money in the bank for approximately 12.1 years to reach $14,300.
Solution
To find the time it takes for the person’s investment to reach $14300, we can use the formula for compound interest:
Given:
- Initial investment
dollars - Annual interest rate
- Compounded annually, so
- Final amount
dollars
We need to solve for
Substitute the given values into the formula:
Now, we can solve for
Solve the equation by following steps:
Solve the equation by following steps:
- step0: Solve for
:
- step1: Simplify:
- step2: Swap the sides:
- step3: Multiply by the reciprocal:
- step4: Multiply:
- step5: Take the logarithm of both sides:
- step6: Evaluate the logarithm:
- step7: Transform the expression:
The solution foris:
Now, we can calculate the value of
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
The person needs to leave the money in the bank for approximately 12.1 years until it reaches $14300.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Bonus Knowledge
To solve the problem using the formula for compound interest
-
Set up the equation:
-
Simplifying gives:
-
Divide both sides by 7500:
-
Taking the natural logarithm:
-
Solve for
:
So, the person must leave the money in the bank for approximately 12.1 years.
Investing has become a pivotal part of financial planning, and understanding how compound interest works can significantly impact long-term savings. You’re essentially “earning interest on interest,” which means the sooner you start saving, the more you benefit! This concept was first popularized in the 17th century by mathematicians like Jacob Bernoulli, who believed that compound interest could demonstrate the concept of exponential growth.
When working with compound interest problems, one common mistake is forgetting to convert percentages into decimal form. Always remember to divide the percentage rate by 100 (e.g.,
