Suppose that $1,000 is invested at 5% interest compounded continuously. Use the formula A = Pert. (a) How long (to the nearest day) before the value is $1,250? 4 v years, 167 x days (b) How long (to the nearest day) before the money doubles? 13 v years, 315 days (c) What is the interest rate (compounded continuously and rounded to the nearest tenth of a percent) if the money doubles in 5 years? 13.86
Suppose that $1,000 is invested at 5% interest compounded continuously. Use the formula A = Pert. (a) How long (to the nearest day) before the value is $1,250? 4 v years, 167 x days (b) How long (to the nearest day) before the money doubles? 13 v years, 315 days (c) What is the interest rate (compounded continuously and rounded to the nearest tenth of a percent) if the money doubles in 5 years? 13.86
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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![Suppose that $1,000 is invested at 5% interest compounded continuously. Use the formula:
\[ A = Pe^{rt} \]
(a) **How long (to the nearest day) before the value is $1,250?**
- **Years:** 4 ✔️
- **Days:** 167 ❌
(b) **How long (to the nearest day) before the money doubles?**
- **Years:** 13 ✔️
- **Days:** 315 ✔️
(c) **What is the interest rate (compounded continuously and rounded to the nearest tenth of a percent) if the money doubles in 5 years?**
- **Interest Rate:** 13.86% ✔️
### Explanation:
In this exercise, you're given a compound interest problem with continuous compounding. The formula \( A = Pe^{rt} \) is used where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (in decimal).
- \( t \) is the time the money is invested or borrowed for, in years.
**Graphs and diagrams**: This image contains text only. There are check marks (✔️) and a cross (❌) indicating correct and incorrect answers respectively, but no graphs or diagrams are present.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F674b5627-6eeb-4539-9ecd-a1ecdabb7121%2F731e4291-bcb6-4eda-923c-8e5aac63c502%2Fh06q6pe_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that $1,000 is invested at 5% interest compounded continuously. Use the formula:
\[ A = Pe^{rt} \]
(a) **How long (to the nearest day) before the value is $1,250?**
- **Years:** 4 ✔️
- **Days:** 167 ❌
(b) **How long (to the nearest day) before the money doubles?**
- **Years:** 13 ✔️
- **Days:** 315 ✔️
(c) **What is the interest rate (compounded continuously and rounded to the nearest tenth of a percent) if the money doubles in 5 years?**
- **Interest Rate:** 13.86% ✔️
### Explanation:
In this exercise, you're given a compound interest problem with continuous compounding. The formula \( A = Pe^{rt} \) is used where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (in decimal).
- \( t \) is the time the money is invested or borrowed for, in years.
**Graphs and diagrams**: This image contains text only. There are check marks (✔️) and a cross (❌) indicating correct and incorrect answers respectively, but no graphs or diagrams are present.
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