I am confused about the order of operations on this equation here. In what order do I need to move the various variables? Could you give me a step-by-step illustration as oppesed to simply the final answer for this equation?Please see the image for the particular problem. Otherwise it is Problem 5P from Chapter 7 (Rate of Return) in Contemporary Engineering Economics 6th Edition. **Explanation of Solution**The time period is denoted by \( n \) and the interest rate is denoted by \( i \). The return on investment can be calculated using the following formula:\[\text{Spending} = \text{Save}_{\text{Annual}} \left( \frac{(1+i)^n - 1}{i(1+i)^n} \right)\]In this scenario:\[2,500,000 = 1,200,000 \left( \frac{(1+i)^{10} - 1}{i(1+i)^{10}} \right)\]Solving for \( i \):\[i = 0.4698\]Therefore, the return on investment is 46.98%.This formula represents the present value of an annuity, providing a way to calculate periodic savings needed for a future spending goal when dealing with compounded interest.

For higher power of polynomials such as given in the question, solution is only feasible with…

Answered: Explanation of Solution Time period is…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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I am confused about the order of operations on this equation here. In what order do I need to move the various variables? Could you give me a step-by-step illustration as oppesed to simply the final answer for this equation?

Please see the image for the particular problem. Otherwise it is Problem 5P from Chapter 7 (Rate of Return) in Contemporary Engineering Economics 6th Edition.

**Explanation of Solution**

The time period is denoted by \( n \) and the interest rate is denoted by \( i \). The return on investment can be calculated using the following formula:

\[
\text{Spending} = \text{Save}_{\text{Annual}} \left( \frac{(1+i)^n - 1}{i(1+i)^n} \right)
\]

In this scenario:

\[
2,500,000 = 1,200,000 \left( \frac{(1+i)^{10} - 1}{i(1+i)^{10}} \right)
\]

Solving for \( i \):

\[
i = 0.4698
\]

Therefore, the return on investment is 46.98%.

This formula represents the present value of an annuity, providing a way to calculate periodic savings needed for a future spending goal when dealing with compounded interest.

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