52 You are the loan shark. What is $1 worth after a year of continuous compounding at 1% per day?
52 You are the loan shark. What is $1 worth after a year of continuous compounding at 1% per day?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Problem 52: Continuous Compounding
**Question:**
You are the loan shark. What is $1 worth after a year of continuous compounding at 1% per day?
**Explanation:**
This problem explores the concept of continuous compounding, a mathematical model for accruing interest. Continuous compounding assumes that interest is being added constantly, rather than at discrete intervals (such as daily, monthly, or yearly). The formula for calculating the future value using continuous compounding is:
\[ A = Pe^{rt} \]
where:
- \( A \) is the future value,
- \( P \) is the principal amount (initial amount of money),
- \( e \) is the base of the natural logarithm (approximately 2.71828),
- \( r \) is the interest rate (expressed as a decimal),
- \( t \) is the time in years.
**Calculation:**
Given:
- \( P = 1 \) (the initial amount),
- \( r = 0.01 \times 365 \) (converting 1% per day into a yearly rate),
- \( t = 1 \) year.
You will substitute these values into the formula to find \( A \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F892e817a-9b32-4eeb-b8fc-5dd7ffde6479%2F82d1e4b9-186e-4e86-94cd-fe0fffe0a09b%2Foplqfq8_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 52: Continuous Compounding
**Question:**
You are the loan shark. What is $1 worth after a year of continuous compounding at 1% per day?
**Explanation:**
This problem explores the concept of continuous compounding, a mathematical model for accruing interest. Continuous compounding assumes that interest is being added constantly, rather than at discrete intervals (such as daily, monthly, or yearly). The formula for calculating the future value using continuous compounding is:
\[ A = Pe^{rt} \]
where:
- \( A \) is the future value,
- \( P \) is the principal amount (initial amount of money),
- \( e \) is the base of the natural logarithm (approximately 2.71828),
- \( r \) is the interest rate (expressed as a decimal),
- \( t \) is the time in years.
**Calculation:**
Given:
- \( P = 1 \) (the initial amount),
- \( r = 0.01 \times 365 \) (converting 1% per day into a yearly rate),
- \( t = 1 \) year.
You will substitute these values into the formula to find \( A \).
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