Week 4: Student Discussion and Response

Initial Investment

Mostly for self-regarding reasons, some of our children are arguing their mom and I really need to invest in a state-of-the-art Airstream Base Camp Trailer with a retail value in 12 years of approximately $37,000.

The Basecamp is allegedly made for those who want to see the world. There is a manufacturer’s promise that it is built for adventure. And the Basecamp trailer is supposedly tough enough to go anywhere our desire to travel attempts to take us, and is comfortable enough to help us enjoy the time once we arrive wherever it is we are supposedly going; or more appropriately, when our children get there. If today’s Basecamp design is already cool, then in 12 years it just might be ready to fly on its own. And with seven children living throughout the United States, the idea of spending six months out of every year bouncing from home-to-home sounds like a fascinating life in retirement, which certainly outplays sitting around watching reality TV shows and mowing the lawn once a week.

I am confident that we can secure a 6% rate of interest. What we are asked to figure out is how much money is required to put into an investment today to have the $37,000 in cash at the end of 12 years.

The desired item is an Airstream Basecamp pull-behind trailer
The cost is 12 years will be approximately $37,000
The average interest rate of the investment is expected to be 6%
The Present Value Formula – P = A(1 +r)-n , where P is the present value that will amount to A dollars in n years at an interest rate r compounded annually

P = A(1+r)-n

The Present Value Formula

P = 37000(1+.06)-12

I inserted the applicable numbers into the PVF in order to begin working through this equation that would enable me to eventually discover my upfront investment that would make it possible at the end of 12 years to purchase in cash the Airstream Base Camp Trailer.

P = 37000(1.06)-12

Starting within the parentheses I multiplied 1x .06(%) to arrive at 1.06

What to do with a Negative Exponent?

The Negative POWER Rule states in this situation: r -12 = 37000

1.0612

I nearly fainted when I saw the negative exponent and originally assumed I would multiply that part of the equation by -12. But thankfully my intuition told me to check in with the Khan Academy and learned how a NEGATIVE EXPONENT means how many times to divide by that number. This lesson is an expansion of my understanding of the RULES OF EXPONENTS. In this context division is the inverse (opposite) of Multiplying a negative exponent. (Khan, 2017)

P = 37000

(1.06)12

The negative exponent creates a RECIPROCAL of the base number and the exponent is applied to the base number of 1.06 representing my expected interest rate and thereby changes is POSITION.

P = 37000

2.012196

My anticipated cost in 12 years, $37,000 is divided by the interest rate after it is multiplied to the 12 power.

P = 18,388

Using this Present Value Formula, the value for P = 18,388

$18,388

This represents our initial investment with an estimated annual average interest rate of 6% over 12 years that will grow to $37,000 for our children’s Airstream Basecamp Trailer.

Khan, S. (2017). Negative exponents. Retrieved March 09, 2017, from

https://www.khanacademy.org/math/pre-algebra/pre-algebra-exponents-radicals/pre-algebra-negative-exponents/v/negative-exponents