INSTRUCTOR GUIDANCE EXAMPLE: Week Four Discussion
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 n. Then it will divide A instead of multiplying A as it seems to be
P = A(1 + r)-n
P = 8000(1 + .09)-12
P = 8000(1.09)-12
P = 8000
P = 8000
P = 2844.28
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.
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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