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**

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**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.
Transcribed Image Text:**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,

       FV=80001+4.5%10    =80001+920010    =8000·2091020010    =20910224·517    12423.75537

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