Finite Mathematics and Applied Calculus

Stefan Waner, Steven Costenoble

Chapter 5

The Mathematics of Finance - all with Video Answers

Educators

Section 1

Simple Interest

Problem 1

Compute the simple interest for the specified period and the future value at the end of the period. Round all answers to the nearest cent.
$$
\$ 2,000 \text { is invested for } 1 \text { year at } 6 \% \text { per year }
$$

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 2

Compute the simple interest for the specified period and the future value at the end of the period. Round all answers to the nearest cent.
$$
\$ 1,000 \text { is invested for } 10 \text { years at } 4 \% \text { per year. }
$$

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 3

Compute the simple interest for the specified period and the future value at the end of the period. Round all answers to the nearest cent.
$$
\$ 20,200 \text { is invested for } 6 \text { months at } 5 \% \text { per year. }
$$

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 4

Compute the simple interest for the specified period and the future value at the end of the period. Round all answers to the nearest cent.
$$
\$ 10,100 \text { is invested for } 3 \text { months at } 11 \% \text { per year. }
$$

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 5

Compute the simple interest for the specified period and the future value at the end of the period. Round all answers to the nearest cent.
$$
\text { You borrow } \$ 10,000 \text { for } 10 \text { months at } 3 \% \text { per year. }
$$

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 6

Compute the simple interest for the specified period and the future value at the end of the period. Round all answers to the nearest cent.
$$
\text { You borrow } \$ 6,000 \text { for } 5 \text { months at } 9 \% \text { per year. }
$$

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 7

Find the present value of the given investment.
An investment earns $2 \%$ per year and is worth $\$ 10,000$ after
5 years.

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 8

Find the present value of the given investment.
An investment earns $5 \%$ per year and is worth $\$ 20,000$ after 2 years.

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 9

Find the present value of the given investment.
An investment earns $7 \%$ per year and is worth $\$ 1,000$ after 6 months.

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 10

Find the present value of the given investment.
An investment earns $10 \%$ per year and is worth $\$ 5,000$ after 3 months.

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 11

Find the present value of the given investment.
An investment earns $3 \%$ per year and is worth $\$ 15,000$ after 15 months.

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 12

Find the present value of the given investment.
An investment earns $6 \%$ per year and is worth $\$ 30,000$ after 20 months.

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 13

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Simple Loans You take out a 6 -month, $\$ 5,000$ loan at $8 \%$ simple interest. How much would you owe at the end of the 6 months?

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 14

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Simple Loans You take out a 15 -month, $\$ 10,000$ loan at $11 \%$ simple interest. How much would you owe at the end of the 15 months?

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 15

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Savings How much would you have to deposit in an account earning $4.5 \%$ simple interest if you wanted to have $\$ 1,000$ after 6 years?

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 16

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Simple Loans Your total payment on a 4 -year loan, which charged $9.5 \%$ simple interest, amounted to $\$ 30,360$. How much did you originally borrow?

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 17

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Bonds A 5-year bond costs $\$ 1,000$ and will pay a total of $\$ 250$ interest over its lifetime. What is its annual interest rate?

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 18

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
\mathrm{\{} B o n d s ~ A ~ 4 - y e a r ~ b o n d ~ c o s t s ~ $\$ 10,000$ and will pay a total of
$\$ 2,800$ in interest over its lifetime. What is its annual interest rate?

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 19

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
\mathrm{\{} T r e a s u r y ~ B i l l s ~ I n ~ D e c e m b e r ~ 2008 (in the midst of the finan-
cial crisis) a $\$ 5,0006$ -month T-bill was selling at a discount rate of only $0.25 \% .{ }^{1}$ What was its simple annual yield?

Carson Merrill

Numerade Educator

Problem 20

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Treasury Bills In December 2008 (in the midst of the financial crisis) a \15,000 3-month T-bill was selling at a discount rate of only $0.06 \% .{ }^{2}$ What was its simple annual yield?

Carson Merrill

Numerade Educator

Problem 21

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Simple Loans A 4,000 loan, taken now, with a simple interest rate of $8 \%$ per year, will require a total repayment of 4,640. When will the loan mature?

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 22

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
$$
\begin{aligned}
&\text { \mathrm{\{} S i m p l e ~ L o a n s ~ T h e ~ s i m p l e ~ i n t e r e s t ~ o n ~ a ~ } \$ 1,000 \text { loan at } 8 \%\\
&\text { per year amounted to } \$ 640 \text { . When did the loan mature? }
\end{aligned}
$$

Subhadeepta Sahoo

Subhadeepta Sahoo

Numerade Educator

Problem 23

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
\mathrm{\{} T r e a s u r y ~ B i l l s ~ A t ~ a u c t i o n ~ o n ~ A u g u s t ~ $18,2005,6$ -month
T-bills were sold at a discount of $3.705 \% .{ }^{3}$ What was the simple annual yield?

Carson Merrill

Numerade Educator

Problem 24

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
\mathrm{\{} T r e a s u r y ~ B i l l s ~ A t ~ a u c t i o n ~ o n ~ A u g u s t ~ $18,2005,3$ -month
T-bills were sold at a discount of $3.470 \% .{ }^{4}$ What was the simple annual yield?

Carson Merrill

Numerade Educator

Problem 25

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Fees You are expecting a tax refund of 1,000$ in 4 weeks. A tax preparer offers you a $\$ 1,000$ loan for a fee of $\$ 50 to be repaid by your refund check when it arrives in 4 weeks. Thinking of the fee as interest, what simple interest rate would you be paying on this loan?

Carson Merrill

Numerade Educator

Problem 26

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Fees You are expecting a tax refund of 1,500 in 3 weeks. A tax preparer offers you a $\$ 1,500$ loan for a fee of $\$ 60$ to be repaid by your refund check when it arrives in 3 weeks. Thinking of the fee as interest, what simple interest rate would you be paying on this loan?

Carson Merrill

Numerade Educator

Problem 27

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Fees You take out a 2-year, 5,000$ loan at $9 \% simple annual interest. The lender charges you a $\$ 100 fee. Thinking of the fee as additional interest, what is the actual annual interest rate you will pay?

Carson Merrill

Numerade Educator

Problem 28

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest $0.001 \%$, as appropriate.
Fees You take out a 3-year, 7,000 loan at 8\% simple annual interest. The lender charges you a $\$ 100$ fee. Thinking of the fee as additional interest, what is the actual annual interest rate you will pay?

Carson Merrill

Numerade Educator

Problem 29

Calculate to the nearest $0.01 \%$ your annual percentage loss (on a simple interest basis) if you had bought Apple stock in June and sold in December.

Carson Merrill

Numerade Educator

Problem 30

Calculate to the nearest $0.01 \%$ your annual percentage return (on a simple interest basis) if you had bought Apple stock in February and sold in June.

Carson Merrill

Numerade Educator

Problem 31

Suppose you bought Apple stock in January 2008 . If you later sold at one of the marked dates on the chart, which of those dates would have given you the largest annual return (on a simple interest basis), and what would that return have been?

Carson Merrill

Numerade Educator

Problem 32

Suppose you bought Apple stock in April. If you later sold at one of the marked dates on the chart, which of those dates would have given you the largest annual loss (on a simple interest basis), and what would that loss have been?

Carson Merrill

Numerade Educator

Problem 33

Did Apple's stock undergo simple interest change in the period January through April? (Give a reason for your answer.)

Carson Merrill

Numerade Educator

Problem 34

If Apple's stock had undergone simple interest change from April to June at the same simple rate as from March to April, what would the price have been in June?

Carson Merrill

Numerade Educator

Problem 35

At what annual (simple interest) rate did the population of San Diego County increase from 1950 to $2000 ?$

Carson Merrill

Numerade Educator

Problem 36

At what annual (simple interest) rate did the population of San Diego County increase from 1950 to $1990 ?$

Carson Merrill

Numerade Educator

Problem 37

If you used your answer to Exercise 35 as the annual (simple interest) rate at which the population was growing since 1950 , what would you predict the San Diego County population to be in $2010 ?$

Carson Merrill

Numerade Educator

Problem 38

If you used your answer to Exercise 36 as the annual (simple interest) rate at which the population was growing since 1950 , what would you predict the San Diego County population to be in $2010 ?$

Carson Merrill

Numerade Educator

Problem 39

Use your answer to Exercise 35 to give a linear model for the population of San Diego County from 1950 to 2000 . Draw the graph of your model over that period of time.

Carson Merrill

Numerade Educator

Problem 40

Use your answer to Exercise 36 to give a linear model for the population of San Diego County from 1950 to 2000 . Draw the graph of your model over that period of time.

Carson Merrill

Numerade Educator

Problem 41

One or more of the following graphs represent the future value of an investment earning simple interest. Which one(s)? Give the reason for your choice(s).

Carson Merrill

Numerade Educator

Problem 42

Given that $F V=5 t+400$, for what interest rate is this the equation of future value (in dollars) as a function of time $t$ (in years)?

Carson Merrill

Numerade Educator

Problem 43

Interpreting the News You hear the following on your local radio station's business news: "The economy last year grew by $1 \%$. This was the second year in a row in which the economy showed a $1 \%$ growth." Because the rate of growth was the same two years in a row, this represents simple interest growth, right? Explain your answer.

Carson Merrill

Numerade Educator

Problem 44

Interpreting the News You hear the following on your local radio station's business news: "The economy last year grew by $1 \%$. This was the second year in a row in which the economy showed a $1 \%$ growth." This means that, in dollar terms, the economy grew more last year than the year before. Why?

Monica Miller

Numerade Educator

Problem 45

Explain why simple interest is not the appropriate way to measure interest on a savings account that pays interest directly into your account.

Monica Miller

Numerade Educator

Problem 46

Suppose that a one-year T-bill sells at a discount rate $d$. Find a formula, in terms of $d$, for the simple annual interest rate $r$ the bill will pay.

Carson Merrill

Numerade Educator