Assume that there are no deposits or withdrawals. An initial deposit of $30,000 grows at an annual rate of 6% for 25 years. Compare the final balances resulting from annual compounding and continuous compounding. (Round your answers to the nearest cent.) annual compounding -128756.13 X continuous compounding $ 134450.67

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Comparison of Annual and Continuous Compounding

Assume that there are no deposits or withdrawals.

An initial deposit of **$30,000** grows at an annual rate of **6%** for **25** years. Compare the final balances resulting from annual compounding and continuous compounding. (Round your answers to the nearest cent.)

#### Annual Compounding
Final Balance: **$128,756.13** ❌

#### Continuous Compounding
Final Balance: **$134,450.67** ✔

In this scenario, continuous compounding yields a higher final balance compared to annual compounding. 

#### Explanation:
- **Annual Compounding**: Interest is added once per year.
- **Continuous Compounding**: Interest is calculated and added continuously, resulting in slightly higher returns over the same period.
Transcribed Image Text:### Comparison of Annual and Continuous Compounding Assume that there are no deposits or withdrawals. An initial deposit of **$30,000** grows at an annual rate of **6%** for **25** years. Compare the final balances resulting from annual compounding and continuous compounding. (Round your answers to the nearest cent.) #### Annual Compounding Final Balance: **$128,756.13** ❌ #### Continuous Compounding Final Balance: **$134,450.67** ✔ In this scenario, continuous compounding yields a higher final balance compared to annual compounding. #### Explanation: - **Annual Compounding**: Interest is added once per year. - **Continuous Compounding**: Interest is calculated and added continuously, resulting in slightly higher returns over the same period.
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