The future value in thousands of dollars of an annuity with a monthly payment of $575 and an annual returns of 3.4%, 5.8% and 2.2% over a number of months follows. 320 280- 240- 200- 160 120 80 40- 36 72 108 144 180 216 252 288 324 360 Match the rate with its color. 5.8 2.2 3.4 a. blue b. green c. purple

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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**Future Value of Annuities**

This educational graph displays the future value, in thousands of dollars, of an annuity with a monthly payment of $575 over various periods, considering annual returns of 3.4%, 5.8%, and 2.2%. The time is measured in months up to 360 months (30 years).

**Graph Details:**

- The horizontal axis represents time in months, labeled in increments from 36 to 360.
- The vertical axis shows the future value in thousands of dollars, ranging from 0 to 360.

**Curves Explanation:**

- **Blue Curve:** Represents a 5.8% annual return. It shows the highest growth over time, reaching above $320,000 by 360 months.
- **Purple Curve:** Represents a 3.4% annual return. It shows moderate growth over the same period, surpassing $240,000 by the end.
- **Green Curve:** Represents a 2.2% annual return. This curve has the slowest growth, ending just under $200,000 by 360 months.

**Matching Rates with Colors:**

- 5.8% - **Blue**
- 2.2% - **Green**
- 3.4% - **Purple**

This visualization helps in understanding how different interest rates impact the future value of an annuity over time.
Transcribed Image Text:**Future Value of Annuities** This educational graph displays the future value, in thousands of dollars, of an annuity with a monthly payment of $575 over various periods, considering annual returns of 3.4%, 5.8%, and 2.2%. The time is measured in months up to 360 months (30 years). **Graph Details:** - The horizontal axis represents time in months, labeled in increments from 36 to 360. - The vertical axis shows the future value in thousands of dollars, ranging from 0 to 360. **Curves Explanation:** - **Blue Curve:** Represents a 5.8% annual return. It shows the highest growth over time, reaching above $320,000 by 360 months. - **Purple Curve:** Represents a 3.4% annual return. It shows moderate growth over the same period, surpassing $240,000 by the end. - **Green Curve:** Represents a 2.2% annual return. This curve has the slowest growth, ending just under $200,000 by 360 months. **Matching Rates with Colors:** - 5.8% - **Blue** - 2.2% - **Green** - 3.4% - **Purple** This visualization helps in understanding how different interest rates impact the future value of an annuity over time.
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