A principal amount of $1500 is placed into a savings account with an APR of 2.55% simple interest for 10 years. The same principal is placed into a savings account with an APR of 3.15% compounded continuously for 7 years. How do I solve this equation? And what formulas should I use? Please show me step by step.
A principal amount of $1500 is placed into a savings account with an APR of 2.55% simple interest for 10 years. The same principal is placed into a savings account with an APR of 3.15% compounded continuously for 7 years. How do I solve this equation? And what formulas should I use? Please show me step by step.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A principal amount of $1500 is placed into a savings account with an APR of 2.55% simple interest for 10 years. The same principal is placed into a savings account with an APR of 3.15% compounded continuously for 7 years.
How do I solve this equation? And what formulas should I use? Please show me step by step.
![### Interest Formulas
This section outlines various mathematical formulas used to calculate interest, including simple interest, compound interest, and continuously compounded interest.
1. **Simple Interest**
The formula for calculating simple interest is:
\[
A = P(rt + 1)
\]
- \( A \) represents the total amount accrued after interest.
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (as a decimal).
- \( t \) is the time in years.
2. **Compound Interest**
The formula for calculating compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
- \( A \) is the total amount accrued after interest.
- \( P \) is the principal amount.
- \( r \) is the annual interest rate (as a decimal).
- \( n \) is the number of times the interest is compounded per year.
- \( t \) is the time in years.
3. **Continuously Compounded Interest**
The formula for continuously compounded interest is:
\[
A = Pe^{rt}
\]
- \( A \) is the total amount accrued after interest.
- \( P \) is the principal amount.
- \( r \) is the annual interest rate (as a decimal).
- \( t \) is the time in years.
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
This information covers the calculation methods for different types of interest rates and their applications across financial contexts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59feeef4-6b05-42eb-a363-2266e2a8ff66%2Fc99f6943-6530-4527-9ba1-2286e5dab42f%2Fk90jalq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Interest Formulas
This section outlines various mathematical formulas used to calculate interest, including simple interest, compound interest, and continuously compounded interest.
1. **Simple Interest**
The formula for calculating simple interest is:
\[
A = P(rt + 1)
\]
- \( A \) represents the total amount accrued after interest.
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (as a decimal).
- \( t \) is the time in years.
2. **Compound Interest**
The formula for calculating compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
- \( A \) is the total amount accrued after interest.
- \( P \) is the principal amount.
- \( r \) is the annual interest rate (as a decimal).
- \( n \) is the number of times the interest is compounded per year.
- \( t \) is the time in years.
3. **Continuously Compounded Interest**
The formula for continuously compounded interest is:
\[
A = Pe^{rt}
\]
- \( A \) is the total amount accrued after interest.
- \( P \) is the principal amount.
- \( r \) is the annual interest rate (as a decimal).
- \( t \) is the time in years.
- \( e \) is the base of the natural logarithm, approximately equal to 2.71828.
This information covers the calculation methods for different types of interest rates and their applications across financial contexts.
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