Sandra and Michael Wilson are the parents of Rory who just turned 5 years old (coincidentally on the same date that primary, secondary and university academic years commence). They own a four-bedroom home in Edinburgh. Sandra is a partner in a local dental practice and Michael is a stay at home dad. Sandra earns £100,000 a year (after tax).

Now that Rory is starting primary school, thoughts have turned to saving for his education. Rory is enrolled to attend a state (i.e. non fee-paying) primary school. The Wilsons plan to send Rory to a private secondary school (when he turns 11). The school is prestigious and its fees are set accordingly. Currently tuition is £20,000 per school year and are projected to rise at the rate of inflation. Currently around 2% per annum.

The Wilsons hope that Rory will subsequently attend their alma mater, Oxford University when he turns 18. Most undergraduate courses at Oxford have a four academic year duration. Undergraduate fees at Oxford are currently £9250 per annum and are projected to rise faster than inflation, at a rate of 4% per annum. In addition, as Rory would be living away from home if he attended Oxford, his parents envisage that his living costs (primarily student accommodation and food) would amount to £10,000 per annum (expressed in today’s prices). These living costs are projected to increase at the rate of inflation, 2% per annum.

Using a discount rate of 7%, what is the present value of the combined projected spend on Rory’s private school fees, university tuition and living costs? (Assume that all fees and living costs are incurred at the beginning of each academic year e.g. Rory’s first school fee invoice will arrive in exactly 6 years which coincides with his first day at secondary school when he turns 11).

The Wilsons plan to fund the expenditure on private school fees from Sandra’s income. They would however like to start investing today in a fund that would be used to pay Rory’s university fees and living costs. They would like to make an equal annual payment into that fund every year (starting in one years’ time) with a view to accumulating £120,000 by Rory’s 18th birthday. This £120,000 would then be drawn down over Rory’s time at Oxford to meet expenses as they come due.

How much money would they have to deposit into the fund every year (with the first payment one year from now) to meet that target assuming a conservative fund return estimate of 3% a year. Will the accumulated amount be enough to cover the joint fees and living costs during Rory’s time at Oxford?

In the Budget Challenge, you had an opportunity to increase or decrease taxes. What changes did you select? Who is helped or harmed by the changes that you proposed? How did the overall debt change as a result of your proposed changes?

What does the slope represent?

Consider the following statements regarding how government spending responds to changes in aggregate income, wealth, and interest rates.

A. Government spending responds directly to changes in aggregate income, wealth, and interest rates. Changes in aggregate income, wealth, and interest rates automatically cause government spending to change.

B. Government spending does not respond directly or indirectly to changes in aggregate income, wealth, or interest rates. Changes in aggregate income, wealth, and interest rates do not have any effect on government spending.

C. Government spending responds indirectly to changes in aggregate income, wealth, or interest rates. During a recession, aggregate income and wealth will fall and the government may decide to increase government spending to stimulate output and jobs in the economy.

Which of the statements are true?

Statement C

Statement A

Statement B

The following data represent the amount of money and invenstor has in an investment account each year for 10 years.

a. Let x=number of years since 1994 and find an exponential regression model of the form y=ab* for this data set, where y is the amount in the account x years since 1994.

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b. If the investor plans on retiring in 2021, what will be the predicted value of this accoutn at that time?

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c. When will the account be worth $50,000?

d. Make a graph of the scatterplot and exponential model below.

Year value of account

1994 $10,000

1995 $10,573

1996 $ 11,260

1997 $11,733

1998 $12,424

1999 $13,269

2000 $13,698

2001 $14,823

2002 $15,297

2003 $16,539

The values of certain types of collectibles can often fluctuate greatly over time. Suppose that the value of a particular limited edition figurine is found to be able to be modeled by the function

?(?) = −0.01?⁴ + 0.47?³ − 7.96?² + 49.18? + 65 for 0 ≤ ? ≤ 20 where ?(?) is in dollars, t is the number of years after the figurine was released, and ? = 0 corresponds to the year 1999.

a) What was the value of the figurine in the year 2009?

b) What was the value of the figurine in the year 2019?

c) What was the instantaneous rate of change of the value of the figurine in the year 2002?

d) What was the instantaneous rate of change of the value of the figurine in the year 2019?

e) Use your answers from parts a-d to estimate the value of the figurine in 2020.