Section 1. Chapter 16
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Challenge: Predicting Savings Growth
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Task
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A financial advisor wants to estimate how a client's savings grow over time when interest is compounded regularly. This type of growth follows a geometric progression, where the savings increase by a constant factor each compounding period.
The total savings can be calculated using the compound interest formula:
A=P(1+nr)ntWhere:
- A — final amount after all interest is applied;
- P — initial deposit;
- r — annual interest rate (as a decimal);
- n — number of compounding periods per year;
- t — time in years;
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Calculate the final savings amount after 20 years using:
- Initial deposit: P=10000.
- Annual interest rate: r=0.08.
- Monthly compounding: n=12.
- Time period: t=20.
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Calculate the total interest earned by subtracting the initial deposit from the final amount.
Solution
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Section 1. Chapter 16
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