Math 1324–________ Name__________________________

A. Martin November 13, 2014

Math for Business Decisions I — Portfolio Problem #3 (Chapter 5)

The Portfolio Problems are designed to give you practice in submitting a professional-looking

presentation of your work. Consequently, you want these documents to reflect your personal

level of excellence to make a good impression with potential business associates. The following

requirements for submitting 1324 Portfolio Problem all s will help you achieve this:

1. All work must be done . You print the portfolio p in pencil only MUST ages and do your work on

those pages, not on other paper. Errors should be fully erased, not marked through. Portfolio

pages MUST be stapled together. Do not attach spiral paper with ragged edges. Neat work

automatically makes a good first impression.

2. All your steps must be shown to receive full credit for your answers. If work is done on the

calculator, you must still show how you set up the problem before entering it into your calculator.

3. Answers requiring complete sentences should include proper capitalization, correct spelling, and

appropriate punctuation. This is formal writing, not texting.

4. Any graphs should be drawn using a straight edge, not sketched free hand. All graphs should be

labeled with the equation or inequality. Ordered pairs should always be in parentheses.

The following problem uses the Chapter 5 skills you have learned to study the issue of saving for

retirement. You may work alone in small groups to or do the work in this problem. You may

use your book, notes, etc. to help you complete the problem, but please do not ask the Math

Outreach Center tutors for help in working this problem. Late portfolio problems will be not

accepted.

Portfolio Problem #3 Due Date: Tuesday, November 25, 2014 at the of Class! Beginning

(The total problem is worth 100 points.)

When people are struggling financially, they often don’t believe that they can make a difference in their

financial security in future years by disciplining themselves to save money regularly now. The goal is

simply too big to tackle when you are struggling to make ends meet every month. Instead, people in

this situation often fall prey to one of two self-defeating behaviors:

A. They invest money in a fantasy like buying lottery tickets with hopes of winning a $30 million

jackpot for an investment of a few dollars’ worth of tickets, , OR

B. They know that trying to win the lottery isn’t practical, so they offer themselves a small, often daily

luxury that they feel they can afford, like a mocha latte from the local coffee house. (Another

example of such an indulgence would be a weekly pedicure.)

Let’s see what happens if we modify those behaviors a little. (Round all of your answers to the

nearest cent.) Math 1324 – Portfolio 3

Page 2 of 3

1. Assume that 25-year-old Denise wastes $10 per week buying lottery tickets, averaging $520 per

year. Now let’s assume that Denise “sees the light” and decides to take that $520 she would have

spent on lottery tickets and deposit it at the end of each year in an annuity paying 6% compounded

annually.

a. How much would Denise have in this annuity after 20 years?

Answer: __________________________________

b. Find the interest her money has earned during that 20 years.

Answer: __________________________________

2. After a couple of years, 27-year-old Denise feels so good about the money she’s been saving instead

of buying futile lottery tickets that she takes investing in herself a step further. To face her

sometimes frustrating job, Denise has typically bought a large mocha latte every day on her way to

work Monday through Friday. She decides to stop buying that coffee just two days a week, and

add that additional $40 she’s saving every month (for a total of $480 a year) to a new Roth IRA

account that pays her 7% compounded monthly.

a. How much would Denise have in this IRA annuity account after 18 years?

Answer: __________________________________ Math 1324 – Portfolio 3

Page 3 of 3

b. Find the interest her money earned during that 18 years.

Answer: __________________________________

3. By now, Denise is 45 years old. She’s got a pretty good job, but she’s starting to think about

retirement and realizing that Social Security just isn’t enough to live on after age 65. Since her

IRA pays a little better interest than that 6% annuity paid (and compounds it more often), she

decides to move all the 6% money into the IRA account with the other money.

a. How much total money does she begin with in the IRA account at this point?

Answer: __________________________________

b. Up to this point, Denise has been saving $1000 a year ($520 + $480 in the two accounts).

Because she’s making better money now, she wants to increase her investment in herself by

putting $150 a month ($1800 a year) into the IRA account on top of the money that’s

already in there. So…how much money will be in total that IRA account in 20 years when

she turns 65?

Answer: ______________________________