# Mat221 week 4 discussion

## Initial Investment

Read the following instructions in order to complete this discussion, and review the example of how to complete the math required for this assignment:

- Think of something you want or need for which you currently do not have the funds. It could be a vehicle, boat, horse, jewelry, property, vacation, college fund, retirement money, or something else. Pick something which cost somewhere between $2000 and $50,000.
- On page 270 of
*Elementary and Intermediate Algebra* you will find the “Present Value Formula,” which computes how much money you need to start with now to achieve a desired monetary goal. Assume you will find an investment which promises somewhere between 5% and 10% interest on your money and you want to purchase your desired item in 12 years. (Remember that the higher the return, usually the riskier the investment, so think carefully before deciding on the interest rate.)
- State the following in your discussion:
- The desired item
- How much it will cost in 12 years
- The interest rate you have chosen to go with from part b

- Set up the formula and work the computational steps one by one, explaining how each step is worked, especially what the negative exponent means. Explain what the answer means.
- Does this formula look familiar to any other formulas you are aware of? If so, which formula(s) and how is it similar?
- Incorporate the following five math vocabulary words into your discussion. Use
**bold** font to emphasize the words in your writing (**Do not write definitions for the words; use them appropriately in sentences describing your math work**.):
- Power
- Reciprocal
- Negative exponent
- Position
- Rules of exponents

Your initial post should be 150-250 words in length. Respond to at least two of your classmates’ posts by Day 7 in at least a paragraph. Do you agree with how they used the vocabulary? Do their answers make sense?

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.

In Section 4.1, we studied the amount formula A = P(1 + r)n. If we are interested in the principal P that must be invested today to grow to a specified amount A in the future, then the principal is called the present value of the investment. We can find a formula for present value by solving the amount formula for P:

Page 270

The Present Value Formula

In Section 4.1, we studied the amount formula A = P(1 + r)n. If we are interested in the principal P that must be invested today to grow to a specified amount A in the future, then the principal is called the present value of the investment. We can find a formula for present value by solving the amount formula for P:

Page 270

The Present Value Formula

In Section 4.1, we studied the amount formula *A* = *P*(1 + *r*)^{n}. If we are interested in the principal *P* that must be invested today to grow to a specified amount *A* in the future, then the principal is called the **present value** of the investment. We can find a formula for present value by solving the amount formula for *P*:

Present Value Formula
The present value *P* that will amount to *A* dollars after *n* years with interest compounded annually at annual interest rate *r* is given by the formula

EXAMPLE **6**
Using the present value formula

A new parent wants to have $20,000 in his child’s college fund when his infant is ready for college in 18 years. How much must he invest now at 8% compounded annually to achieve this goal?

Solution
Use *n* = 18, *A* = $20,000, and *r* = 0.08 in the present value formula:

An investment today of $5004.98 will amount to $20,000 in 18 years.

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