**SAS 4 and SAS 5**

2. Calculate the regression equation for the given data. Graph the regression equation on

the scatterplot. Explain why the function model you used makes sense in the problem

situation.

y= 9062.68*0.9^x

3. Josephine is 20 years old and wants to save $1 million for retirement in 50 years.

Assume she invests in a savings account that earns at least the current rate of

inflation. Determine how much Josephine must save today to reach her retirement

goal.

$1,000,000= PV(1+0.56/1)^50

$1,000,000= PV(1.56)^50

$1,000,000= PV(15.25)

/15.25 /15.25

$65573.77=PV

1. Create a scatterplot of the given data. Label the axes and scales, and provide a title.

5. REFLECTION: Suppose Josephine believes in spending now and saving later. How could

you use the table from Question 4 to convince her otherwise?

The longer Josephine waits to save money for her retirement the larger the sum of the required PV increases.

**Rachel Turner and Nicholle Estevez**

, using

• FV for future value

• t for time (years)

• i for interest rate (in decimal form)

• n for number of compound periods per year

• PV for the principal or present value

6. Blaine wants to have $1,000 in 10 years. The following are the choices in which he can

invest:

• a savings account earning 3% compounded quarterly,

• a checking account earning 1% compounded monthly, or

• a money market account earning 4.5% compounded semiannually.

Blaine plans on making no withdrawals or deposits for 10 years.

Rewrite the formula from Question 3 for present value and allow for any compounding

period (n).

7. Rewrite the present-value formulas for each account that Blaine is considering. Make

sure that the formulas include compounding periods other than annual and incorporate

the different rates.

8. Graph the present-value formula for each account. Label the axes, scales, and curves,

and provide titles.

Which factor has the most significant effect on the curve: the interest rate or

compounding periods? Why?

9. REFLECTION: In which account should Blaine invest? Why?

10. EXTENSION: Locate an article about what investments financial experts are currently

recommending for clients at various times of life (young, middle age, etc.). Prepare a

short presentation to share with the class regarding your findings.

FV=PV(1+i/n)^nt

FV/(1+i/n)^nt=PV

1000/[1+(0.01/12)]^12t= PVchecking

1000/(1+0.03/4)^4t=PV savings

1000/(1+0.045/2)^2t=PVmoneymarket

Interest has the most significant effect because the PV is ordered by interest rates.

Blaine should invest in the money market because it has higher interest and lowest PV.

Young Adults (18-39)

Make compound interest work for you by putting time on your side. If you save $50 a week from age 22 to 65, you’ll have almost $1 million, assuming an 8% average annual return. To learn about investing, visit the Cooperative Extension investing home study course, Investing for Your Future, at www.investing.rutgers.edu.

Middle Aged Adults (40-54)

Continue to make compound interest work for you, especially if you’re making up for lost time. If you save $200 a week from age 45 to age 65, you’ll accumulate about $510,000 assuming an 8% average annual return. For additional “catch-up” strategies, see these tips for late savers.

Age 55 and Older

Upon leaving paid employment, create a “retirement paycheck” with withdrawals from invested assets. Many experts advise withdrawing no more than 4% to 4.5% of assets annually to insure that you will not outlive your money. This amount should then be adjusted annually for inflation. Example: someone with $300,000 of savings would withdraw $12,000 (4% of $300,000) in year one and $12,360 (12,000 + $12,000 x 3% inflation rate) in year two, etc. Keep some stock in your investment portfolio throughout retirement to hedge inflation.

http://www.militarysaves.org/blog/1208-financial-strategies-by-generation-for-young-middle-aged-and-older-adults

The model makes sense because it shows that over time more principal is required if you want the future investment to be a certain amount.

SAS 5 Decision Making in Finance: Present Value of an Investment

VI.B Student Activity Sheet 5: A Cool Tool!

Vanessa is a financial planner specializing in retirement savings. She realizes the importance of using mathematical formulas and the appropriate tools to help her clients understand the reasoning behind the advice she is giving. One of her favorite tools is a time-value-of-money (TVM) calculator. In Student Activity Sheet 4, you met Josephine, one of Vanessa’s clients who wanted to retire with $1 million in savings.

1. In Josephine’s initial situation, she plans to retire in 50 years with $1 million in savings.

Vanessa advised her to find an account that earned at least the current rate of inflation.

Use this information to complete the table below.

Vanessa uses a TVM calculator to help Josephine understand how the different variables affect one another.

2. Identify the values in Josephine’s situation for each variable that the TVM calculator uses.

3. Use the TVM calculator to determine the present value (PV) of the investment required to meet Josephine’s retirement goal. How does this amount compare to what you determined in Student Activity Sheet 4?

The PV of the investment required to meet her retirement goal is $65584.93 which is the same as Sheet 4

Use the TVM calculator to answer the following questions for some of Vanessa’s other clients.

4. Reginald wants to find the future value of an investment of $6,000 that earns 6.25% compounded quarterly for 35 years.

5. Hilda wants to have $10,000 in 10 years after investing in an account that earns 3.6% compounded monthly.

6. Juan wants to invest $1,250 in an account that earns 2.34% interest, compounded monthly. How many years will it take for the account to have a value of $5,000?

It will take Juan about 711.6 months or 711.6 ÷ 12 = 59.3 years for his investment of $1,250 at 2.34% compounded monthly to be worth $5,000.

7. Another of Vanessa’s clients, Ronnie, wants to save for retirement. Ronnie believes that he will need $2,000,000, since he is planning to be retired for 20 to 30 years. He can save in investments that have the following parameters:

• The number of years to save is 20 to 40.

• The number of compounding periods is annually, quarterly, monthly, weekly, and daily.

• The interest rate can be 2.77% to 5.23% or any rate between.

Ronnie wants to know the effect that each variable has on the present value. Select a variable, and use the following steps to complete the table below:

• Start with the minimum value of your variable.

• Use the average value of the other variables that have parameters.

• Calculate the present value of the investment.

• Decide the next value of your variable to test and repeat the process for a total of five different values.

Overall, what impact on the present value does each variable have?

The variable in the first graphs did not have an effect on the PV. The exponent of the equation changes when the variable changes.

THANK YOU

Present Value

Principal Required

Years till Maturity