AMDM TVM 1. Mckenna invests a sum of money in a savings
account with a fixed annual interest rate of
5.41% compounded monthly. After 8 years, the balance reaches
$10,675.76. What was the amount of the
initial investment?

2) Cooper invests $3,472 in a retirement
account with a fixed annual interest rate
compounded 12 times per year. After 20
years, the balance reaches $10,342.33. What is the interest rate of the account?

3) Rebecca invests $1,616 in a savings
account with a fixed annual interest rate of
8.46% compounded continuously. How
long will it take for the account balance to
reach $3,460.30?

4) Sage invests $7,566 in a retirement
account with a fixed annual interest rate of
6.90% compounded 6 times per year. What will the account balance be after 18
years?

5) How much money in interest will you pay
on a $150,000 mortgage paying 3.9%
interest compounded monthly for 18
years?

6) How many years will it take Elizabeth to
pay off a $12,000 credit card bill paying
15.8% interest compounded continuously, if she made a minimum payment of $207 a
month?

7) You finally decide to purchase your first
home. You calculate a monthly budget of
$1100 for a mortgage payment. Your bank
offers you 3.9% interest compounded
annually for 30 years. What is the
maximum price range of houses will you
tell your realtor to look for?

8) Zachary wants to finance a new Ford
truck. He has $458 budgeted a month for
a payment. The truck is $22,500 and his
bank offers him a loan for the amount at
8.52% interest compounded quarterly for
60 months. Can he afford this truck, if not
what is his maximum loan amount he can
afford? Explain

9) Camryn accumulated $19000 in debt from
cosmotology school. Her bank offers her
to refinance the loan at 5.32% interest
compounded daily. She wants to pay this
loan back in 15 years. How much is her
monthly payment? How much interest
was charged for this loan?

10) You and your financial advisor speculate
that the lifestyle at retirement requires a
minimum of $4.5 million. You deposit
$15,000 into a fund yielding 5.4% interest
compounded daily. You also deposit $500
monthly for the next 45 years. Did you
meet your goal, if not what should you
have deposited monthly?

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.

Variable Definition of Variable Value in Josephine’s

Situation

FV future value, or value of the investment at maturity

t number of years of investment until maturity

i annual interest rate (as a decimal)

PV principal, or present value

n number of compounding periods per year

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.

Variable Definition of Variable Value in Josephine’s

Situation

N number of compounding periods between the

time of investment and the time of retirement

I% annual interest rate (as a percent)

PV principal, or present value

PMT amount of each regular payment

FV future value, or value of the investment at

maturity

P/Y

number of payments per year (usually the same

as the number of compounding periods per year,

C/Y)

C/Y number of compounding periods per year

Student: Class: Date:

Decision Making in Finance: Present Value of an Investment

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

Charles A. Dana Center at The University of Texas at Austin Advanced Mathematical Decision Making (2010)

Activity Sheet 5, 6 pages

14

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?

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.

Variable Definition of Variable Value in Reginald’s

Situation

N number of compounding periods between the time

of investment and the time of retirement

I% annual interest rate (as a percent)

PV principal, or present value

PMT amount of each regular payment

FV future value, or value of tStep-by-step explanation:

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step-by-step explanation: