Consider;

1. (a) What is the fundamental reason that money has "time value"?

(b) Does money have time value if inflation rate is zero?

(c) Does money have time value if market interest rate is zero?

1.The couple has combined annual income of $95,000 today. They expect an annual average growth in their income of 3%. How much will they be making annually by the time they retire?

2.They want to retire with $2 million in savings. They also want to set aside a flat $7,000 every year, at the beginning of each year starting now, as savings toward the retirement goal. What does the saving have to grow in value per year in order for them to achieve their retirement goal? They have no savings for this purpose as of today.

3.If the couple want to procrastinate their retirement savings until they reach 35, and if retirement savings will grow at a rate of 8%, how much would they need to save per year, at the end of every year, in order to achieve the $2 million target by the time they retire? They will have no savings for this purpose as they begin their retirement program.

4.Assume they have $15,000 already set aside for the purpose of retirement, how much would they have to save every year, at the beginning of each year starting now, in order to attain the goal of $2 million by the time they retire? Assume they are able to achieve an average rate of return on their savings of 8%.

5.If they have retired with $2 million in savings, and they want to withdraw $120,000 every year for living expenses at the beginning of each year, how long can their retirement nest egg last (in years) if the rate of return on their savings is 5% post-retirement?

6.Answer Question 6 again if they want to leave $1 million to their kids when they die (which is timed to be the date when their savings run out).

7.If they want to leave a full $2 million for their kids by the time they die, which is assumed to be 25 years after retirement, how much can they afford to withdraw per year, at the beginning of each year, if they retire with their $2 million nest egg as planned, and their retirement savings will still grow at 5% per year?

8.The couple plan to have their first kid in exactly 1 year from now. Today a college education costs about $30,000 a year. Assume this education cost grows with at annual inflation rate of 6%. How much will the college education cost per year be when the child turns 18? [Note the number of years elapsed.]

9.They want to find out if college costs $90,000 per year when their child gets into college as he/she turns 18, how much will be the total cost of a college education (that lasts for 4 years) in today's dollars if the cost of money is 8%? Assume you pay the tuitions at the beginning of each year and the annual tuition cost will grow at a 6% annual rate. [Hint: first compute the beginning value (at 19th year) of the tuition payment stream over the 4-year period]

Cause and Effect with Correlations When two variables have a statistical correlation, we cannot tell the direction of causation (which variable might be causing changes in the other). In the following diagrams, X and Y are variables that are statistically correlated. These diagrams illustrate some of the possible cause/effect relationships, [For simplicity, the correlation we shown as positive. These causal pattern sho apply to negative correlations, ] Please label each diagram with the appropriate term: Indirect spurious reverse moderator direct mediator reciprocal third variable X causation X Y causation X Y causation TX Y causation X cousation Y relationship 1 x)[If there is a positive correlation between number of years studying math and ear size (for children). does that prove that larger ears cause more studying of math, or vice versa? Can you think of a hidden variable that might be influencing both of the other variables? Choose the correct answer below. O A. It does not prove causation, because older children have larger ears and have studied math longer. Larger ears do not cause an increase in years of studying. There is no hidden variable. O B. It proves causation, because the two variables are related implying causation. Larger ears cause an increase in years of studying. The hidden variable is age. O C. It does not prove causation, because older children have larger ears and have studied math longer. Larger ears do not cause an increase in years of studying. The hidden variable is age. O D. It proves causation, because the two variables are related implying causation. Larger ears cause an increase in years of studying. There is no hidden variable. Click to select your answer. ? Save for Later O Type here to search 12 15 16 17 esc X @ % 2 3 4 5 OQUESTION 17 If there is a positive correlation between number of years studying a foreign language and shoe size (for children) does that prove that more studying of a foreign language causes one to have larger feet or vice versa> can you think of a hidden variable that might be influencing both of the other variables? Gi It proves causation because the two variables are related, implying causation, More study causes larger feet. There is no fuddon variable. It does not prove causation, because older children have larger feet and have studied foreign language longer. More srudy does not cause larger feet. The hidden variable is age" it proves causation, because the two variables are related, implying causation, More study causes larger feet. The hidden variable is age. It does not prove causation. because older children have larger feet and have studied foreign language longer. More shitty does not calise larger foot. There Is no hidden variableO Mark this question Question 9 Which of the following statements is TRUE? O A high correlation is insufficient to establish causation on its own. O Only a correlation equal to O implies causation. O A correlation of 1 or -1 implies causation. O If the two variables of a scatterplot are strongly related, this condition implies causation between the two variables. SAVE AND CONTINUE 2020 SOPHIA Lonming. LLC SOPHIA is a registered inditrack of SOPHIA Learning, LLC. About Contact Us Privacy Policy Terms of UseQUESTION 16 Economists who believe in the quantity theory of money argue that: O a. the causation in the equation of exchange goes from PQ to MV. Ob. the causation in the equation of exchange goes from MV to PQ. c. the causation in the equation of exchange could go either way. d. there is no causation in the equation of exchange