initial investment

initial investment

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.

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 2

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
Example from instructor

INSTRUCTOR GUIDANCE EXAMPLE: Week Four Discussion Initial Investment
My best friend and her new husband (Fred and Ethel) just got back from their honeymoon which was a trip down the River Nile in Egypt. They are excited about traveling together as a couple and they want to start saving for a very special trip. My own 25th wedding anniversary falls in the same month as Fred and Ethel’s 12th anniversary and they thought it would be fun to plan a trip together. They have done a little research enough to realize we will need about $8,000 per couple set aside for this trip. Fred also found an investment opportunity which promises to have an average return of about 9% per year if one invests long term. We need to know how much each couple needs to invest now to reach their goal in time.
The desired item is travel.
The cost in 12 years will be about $8,000.
The average interest rate of the investment is 9%.
The Present Value Formula is P = A(1 + r)-n where P is the present value that will amount to A dollars in n years at interest rate r compounded annually.
Notice that the quantity raised to a power has the negative exponent of –n. According to the rules of exponents, this means that once the negative is put into effect, the base quantity will change position by dropping down into the denominator where it will be
raised to the power of doing now.
n. Then it will divide A instead of multiplying A as it seems to be
Here are the relevant numbers are plugged into the formula
Add inside the parenthesis
The negative exponent creates the reciprocal of the base number (in other words, changes its position from up top to down below) The exponent is applied to the base number
This is the value of P using the formula.
P = P= P= P=
P= P=
A(1 + r)-n 8000(1 + .09)-12 8000(1.09)-12
8000 (1.09)12
8000 2.81266…
2844.28
Given these results and knowing the interest rate may not stay exactly at 9% we will begin our investment with $3000 right now to begin to save for our big twenty-fifth (and twelfth) anniversary trip. This should give us a little cushion for inflation and such.
[Student answers to the last question will vary depending upon their memory and understanding of formulas they have see in the past.

 
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