**Investment Calculation Problem**---**Problem Statement:**If you invested $8000 at 4.5% interest compounded continuously for 10 years, how much would you have made?--- **Explanation:**This problem involves calculating the future value of an investment using the formula for continuous compounding:\[ A = Pe^{rt} \]Where:- $ A $ is the amount of money accumulated after n years, including interest.- $ P $ is the principal amount ($8000 in this case).- $ r $ is the annual interest rate (decimal) (4.5% or 0.045).- $ t $ is the time the money is invested for in years (10 years).- $ e $ is the base of the natural logarithm, approximately equal to 2.71828.Use this formula to determine how much the investment will grow over a period of 10 years when compounded continuously at 4.5% interest.

Answered: If you invested $800 o at 4.5% interest…

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If you invested $800 o at 4.5% interest Crompounded ceritinuously foe have made ? 10 much weuld years, how you

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

**Investment Calculation Problem**

---

**Problem Statement:**

If you invested $8000 at 4.5% interest compounded continuously for 10 years, how much would you have made?

---

**Explanation:**

This problem involves calculating the future value of an investment using the formula for continuous compounding:

\[ A = Pe^{rt} \]

Where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount ($8000 in this case).
- $ r $ is the annual interest rate (decimal) (4.5% or 0.045).
- $ t $ is the time the money is invested for in years (10 years).
- $ e $ is the base of the natural logarithm, approximately equal to 2.71828.

Use this formula to determine how much the investment will grow over a period of 10 years when compounded continuously at 4.5% interest.

Expert Solution

Step 1

Given:

initial value P = 8000

rate r = 4.5

time t =10 years.

So,

$F V = 8000 {(1 + 4.5 %)}^{10} = 8000 {(1 + \frac{9}{200})}^{10} = 8000 \cdot \frac{209^{10}}{200^{10}} = \frac{209^{10}}{2^{24} \cdot 5^{17}} \approx 12423.75537$

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