Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences

Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Chapter 3 Mathematics of Finance - all with Video Answers

Educators

Chapter Questions

Problem 1

In Problems $1-4$, find the indicated quantity, given $A=P(1+r t)$.
$A=$ ?; $$P=\$ 1,200 ; r=20 \% ; t=2$$ months

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Problem 2

In Problems $1-4$, find the indicated quantity, given $A=P(1+r t)$.
$$A=\$ 808 ; P=? ; r=12 \% ; t=1$$ month

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Problem 3

In Problems $1-4$, find the indicated quantity, given $A=P(1+r t)$.
$$A=\$ 1,020 ; P=\$ 1,000 ; r=8 \% ; t=$$ ?

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Problem 4

In Problems $1-4$, find the indicated quantity, given $A=P(1+r t)$.
$$A=\$ 4,120 ; P=\$ 4,000 ; r=? ; t=6$$ months

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Problem 5

In Problems 5 and 6, find the indicated quantity, given $A=P(1+i)^n$.
$$A=? ; P=\$ 1,200 ; i=0.005 ; n=30$$

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Problem 6

In Problems 5 and 6, find the indicated quantity, given $A=P(1+i)^n$.
$$A=\$ 7,820 ; P=? ; i=0.03 ; n=4$$

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00:26

Problem 7

In Problems 7 and 8 , find the indicated quantity, given $A=P e^n$.
$$A=? ; P=\$ 4,750 ; r=6.8 \% ; t=3$$ years

Erika Bustos

Numerade Educator

Problem 8

In Problems 7 and 8 , find the indicated quantity, given $A=P e^n$.
$$A=\$ 36,000 ; P=$$ ?; $r=9.3 \% ; t=60$ months

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Problem 9

In Problems 9 and 10, find the indicated quantity, given
$$
F V=P M T \frac{(1+i)^n-1}{i}
$$
$$F V=? ; P M T=\$ 3,000 ; i=0.04 ; n=36$$

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Problem 10

In Problems 9 and 10, find the indicated quantity, given
$$
F V=P M T \frac{(1+i)^n-1}{i}
$$
$$F V=\$ 8,000 ; P M T=? ; i=0.015 ; n=48$$

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Problem 11

In Problems 11 and 12, find the indicated quantity, given
$$
P V=P M T \frac{1-(1+i)^{-n}}{i}
$$
$P V=$ ?; $$P M T=\$ 8,000 ; I=0.04 ; n=5$$

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Problem 12

In Problems 11 and 12, find the indicated quantity, given
$$
P V=P M T \frac{1-(1+i)^{-n}}{i}
$$
$$P V=\$ 8,000 ; P M T=? ; i=0.0075 ; n=60$$

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03:35

Problem 13

Solve the equation $2,500=1,000(1.06)^n$ for $n$ to the nearest integer using:
(A) Logarithms
(B) Graphical approximation techniques or an equation solver on a graphing calculator

Ryan Mcalister

Numerade Educator

03:35

Problem 14

Solve the equation
$$
5,000=100 \frac{(1.01)^n-1}{0.01}
$$
for $n$ to the nearest integer using:
(A) Logarithms
(B) Graphical approximation techniques or an equation solver on a graphing calculator.

Ryan Mcalister

Numerade Educator

01:49

Problem 15

A person opened a savings account 3 months ago. Now he has a balance of $$\$ 20,400$$. If the bank pays $8 \%$ simple interest, how much money did he deposit?

Ankit Gupta

Numerade Educator

01:25

Grandparents deposited $$\$ 6,000$$ into a grandchild's account toward a college education. How much money (to the nearest dollar) will be in the account 17 years from now if the account earns $7 \%$ compounded monthly?

Andrew Davis

Numerade Educator

01:21

Problem 17

How much should you pay for a corporate bond paying $6.6 \%$ compounded monthly in order to have $$\$ 25,000$$ in 10 years?

Gregory Higby

Numerade Educator

07:18

Problem 18

Five friends invested $$\$ 10,000$$ each at the same time at an interest rate of $12 \%$ compounded in the following manner:
$$
\begin{array}{lll}
\text { Annually } & \text { Semiannually } & \text { Monthly } \\
\text { Weekly } & \text { Daily }
\end{array}
$$
At the end of a year, which of them earned the highest interest? (Use a 365-day year.)

Bobby Barnes

University of North Texas

Problem 19

One investment pays $13 \%$ simple interest and another $9 \%$ compounded annually. Which investment would you choose? Why?

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01:25

Problem 20

A $$\$ 10,000$$ retirement account is left to earn interest at $7 \%$ compounded daily. How much money will be in the account 40 years from now when the owner reaches 65 ? (Use a 365-day year and round answer to the nearest dollar.)

Andrew Davis

Numerade Educator

01:00

Problem 21

A couple wishes to have $$\$ 40,000$$ in 6 years for the down payment on a house. At what rate of interest compounded continuously must $$\$ 25,000$$ be invested now to accomplish this goal?

Heather Zimmers

Numerade Educator

02:19

Problem 22

Which is the better investment and why: $9 \%$ compounded quarterly or $9.25 \%$ compounded annually?

Emily Frampton

Numerade Educator

03:01

Problem 23

To save for a child's education, a couple decided to invest $$\$ 3,000$$ at the end of each 6-month period in a fund paying $8 \%$ per year compounded semiannually. What is the amount of the investment at the end of 18 years?

Vishal Parmar

Numerade Educator

01:43

Problem 24

A credit card company charges a $22 \%$ annual rate for overdue accounts. How much interest will be owed on a $$\$ 635$$ account 1 month overdue?

Brian Lovejoy

Numerade Educator

01:17

Problem 25

What will a $$\$ 23,000$$ car cost (to the nearest dollar) 5 years from now if the inflation rate over that period averages $5 \%$ compounded annually?

Sanchit Jain

Numerade Educator

01:17

Problem 26

What would the $$\$ 23,000$$ car in Problem 25 have cost (to the nearest dollar) 5 years ago if the inflation rate over that period had averaged $5 \%$ compounded annually?

Sanchit Jain

Numerade Educator

01:01

Problem 27

A loan of $$\$ 2,500$$ was repaid at the end of 10 months with a check for $$\$ 2,812.50$$. What annual rate of interest was charged?

Trinity Steen

Numerade Educator

Problem 28

You want to purchase an automobile for $$\$ 21,600$$. The dealer offers you $0 \%$ financing for 48 months or a $$\$ 3,000$$ rebate. You can obtain $4.8 \%$ financing for 48 months at the local bank. Which option should you choose? Explain.

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02:20

Problem 29

Find the annual percentage yield on a $\mathrm{CD}$ earning $6.25 \%$ if interest is compounded
(A) monthly.
(B) continuously.

Sreeraj P

Numerade Educator

02:00

Problem 30

You have $$\$ 5,000$$ toward the purchase of a boat that will cost $$\$ 6,000$$. How long will it take the $$\$ 5,000$$ to grow to $$\$ 6,000$$ if it is invested at $9 \%$ compounded quarterly? (Round up to the next-higher quarter if not exact.)

Nick Johnson

Numerade Educator

02:30

Problem 31

How long will it take money to double if it is invested at $6 \%$ compounded monthly? 9\% compounded monthly? (Round up to the next-higher month if not exact.)

Priyanka Sadarangani

Numerade Educator

Problem 32

What amount will you receive at the end of 7 years if you deposit $$\$ 7,000$$ payable at the end of each year at an interest rate of $6 \%$ per annum compounded annually?

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01:52

Problem 33

If you just sold a stock for $$\$ 17,388.17$$ (net) that cost you $$\$ 12,903.28$$ (net) 3 years ago, what annual compound rate of return did you make on your investment?

Sheryl Ezze

Numerade Educator

01:41

Problem 34

The table shows the fees for refund anticipation loans (RALs) offered by an online tax preparation firm. Find the annual rate of interest for each of the following loans. Assume a 360-day year.
(A) A $$\$ 400$$ RAL paid back in 15 days
(B) A $$\$ 1,800$$ RAL paid back in 21 days
$$
\begin{array}{|c|c|}
\hline \text { RAL Amount } & \text { RAL Fee } \\
\hline \$ 10-\$ 500 & \$ 29.00 \\
\hline \$ 501-\$ 1,000 & \$ 39.00 \\
\hline \$ 1,001-\$ 1,500 & \$ 49.00 \\
\hline \$ 1,501-\$ 2,000 & \$ 69.00 \\
\hline \$ 2,001-\$ 5,000 & \$ 82.00 \\
\hline
\end{array}
$$

Monica Miller

Numerade Educator

03:13

Problem 35

An investment company pays an interest rate of $8 \%$ per annum compounded quarterly. How much should be deposited with the company at the beginning of each quarter in order to accumulate $$\$ 8,000$$ in 3 years?

Amy Jiang

Numerade Educator

01:26

Problem 36

A person wants to establish an annuity for retirement purposes. He wants to make quarterly deposits for 20 years so that he can then make quarterly withdrawals of $$\$ 5,000$$ for 10 years. The annuity earns $7.32 \%$ interest compounded quarterly.
(A) How much will have to be in the account at the time he retires?
(B) How much should be deposited each quarter for 20 years in order to accumulate the required amount?
(C) What is the total amount of interest earned during the 30-year period?

Breanna Ollech

Numerade Educator

01:07

Problem 37

If you borrow $$\$ 4,000$$ from an online lending firm for the purchase of a computer and agree to repay it in 48 equal installments at $0.9 \%$ interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?

Catt Huth

Numerade Educator

01:52

Problem 38

A company decides to establish a sinking fund to replace a piece of equipment in 6 years at an estimated cost of $$\$ 50,000$$. To accomplish this, they decide to make fixed monthly payments into an account that pays $6.12 \%$ compounded monthly. How much should each payment be?

Charles Carter

Numerade Educator

01:03

Problem 39

What annual rate of interest compounded semiannually should one obtain if one wants to double one's investment in 10 years?

Carson Merrill

Numerade Educator

01:35

Problem 40

A student receives a student loan for $$\$ 8,000$$ at $5.5 \%$ interest compounded monthly to help her finish the last 1.5 years of college. Starting 1 year after finishing college, the student must amortize the loan in the next 5 years by making equal monthly payments. What will the payments be and what total interest will the student pay?

Lourence Gonhovi

Numerade Educator

02:18

Problem 41

If you invest $$\$ 5,650$$ in an account paying $8.65 \%$ compounded continuously, how much money will be in the account at the end of 10 years?

Nick Johnson

Numerade Educator

01:52

Problem 42

A company makes a payment of $$\$ 1,200$$ each month into a sinking fund that earns $6 \%$ compounded monthly. Use graphical approximation techniques on a graphing calculator to determine when the fund will be worth $$\$ 100,000$$.

Charles Carter

Numerade Educator

02:08

Problem 43

A couple has a $$\$ 50,000,20$$-year mortgage at $9 \%$ compounded monthly. Use graphical approximation techniques on a graphing calculator to determine when the unpaid balance will drop below $$\$ 10,000$$.

Liuxi Sun

Numerade Educator

01:14

Problem 44

If interest is compounded continuously, at what nominal rate will an investment of $P$ triple in 12 years?

Steven Clarke

Numerade Educator

04:25

Problem 45

Construct the amortization schedule for a $$\$ 1,000$$ debt that is to be amortized in four equal quarterly payments at $2.5 \%$ interest per quarter on the unpaid balance.

Charles Carter

Numerade Educator

05:35

Problem 46

You can afford monthly deposits of only $$\$ 300$$ into an account that pays $7.98 \%$ compounded monthly. How long will it be until you will have $$\$ 9,000$$ to purchase a used car? (Round to the next-higher month if not exact.)

Sreeraj P

Numerade Educator

05:54

Problem 47

A company establishes a sinking fund for plant retooling in 6 years at an estimated cost of $$\$ 850,000$$. How much should be invested semiannually into an account paying $8.76 \%$ compounded semiannually? How much interest will the account earn in the 6 years?

Amy Jiang

Numerade Educator

04:01

Problem 48

Which is a better investment: $3 \%$ per year compounded monthly, or $3.1 \%$ per year simple interest?

Melissa Salvador

Numerade Educator

01:59

Problem 49

If you buy a 13-week T-bill with a maturity value of $$\$ 5,000$$ for $$\$ 4,922.15$$ from the U.S. Treasury Department, what annual interest rate will you earn?

Brian Lovejoy

Numerade Educator

02:17

Problem 50

In order to save enough money for the down payment on a condominium, a young couple deposits $$\$ 200$$ each month into an account that pays $7.02 \%$ interest compounded monthly. If the couple needs $$\$ 10,000$$ for a down payment, how many deposits will the couple have to make?

Vishal Parmar

Numerade Educator

06:29

Problem 51

A business borrows $$\$ 80,000$$ at $9.42 \%$ interest compounded monthly for 8 years.
(A) What is the monthly payment?
(B) What is the unpaid balance at the end of the first year?
(C) How much interest was paid during the first year?

Stark Ledbetter

Numerade Educator

01:15

Problem 52

You unexpectedly inherit $$\$ 10,000$$ just after you have made the 72 nd monthly payment on a 30-year mortgage of $$\$ 60,000$$ at $8.2 \%$ compounded monthly. Discuss the relative merits of using the inheritance to reduce the principal of the loan or to buy a certificate of deposit paying $7 \%$ compounded monthly.

Breanna Ollech

Numerade Educator

01:23

Problem 53

Your parents are considering a $$\$ 75,000,30$$-year mortgage to purchase a new home. The bank at which they have done business for many years offers a rate of $7.54 \%$ compounded monthly. A competitor is offering $6.87 \%$ compounded monthly. Would it be worthwhile for your parents to switch banks? Explain.

Narayan Hari

Numerade Educator

01:33

Problem 54

How much should a $$\$ 5,000$$ face value zero coupon bond, maturing in 5 years, be sold for now, if its rate of return is to be $5.6 \%$ compounded annually?

Matthew Wagner

Numerade Educator

03:04

Problem 55

If you pay $$\$ 5,695$$ for a $$\$ 10,000$$ face value zero coupon bond that matures in 10 years, what is your annual compound rate of return?

Mike Stern

Numerade Educator

01:28

Problem 56

If an investor wants to earn an annual interest rate of $6.4 \%$ on a 26-week T-bill with a maturity value of $$\$ 5,000$$, how much should the investor pay for the T-bill?

Kaylee Mcclellan

Numerade Educator

01:37

Problem 57

Two years ago you borrowed $$\$ 10,000$$ at $12 \%$ interest compounded monthly, which was to be amortized over 5 years. Now you have acquired some additional funds and decide that you want to pay off this loan. What is the unpaid balance after making equal monthly payments for 2 years?

Monica Miller

Numerade Educator

01:11

Problem 58

What annual nominal rate compounded monthly has the same annual percentage yield as $7.28 \%$ compounded quarterly?

Manisha Sarker

Numerade Educator

00:00

Problem 59

(A) A man deposits $$\$ 2,000$$ in an IRA on his 21 st birthday and on each subsequent birthday up to, and including, his 29th (nine deposits in all). The account earns $8 \%$ compounded annually. If he leaves the money in the account without making any more deposits, how much will he have on his 65 th birthday, assuming the account continues to earn the same rate of interest?
(B) How much would be in the account (to the nearest dollar) on his 65th birthday if he had started the deposits on his 30 th birthday and continued making deposits on each birthday until (and including) his 65 th birthday?

Andrew Lee

Numerade Educator

00:34

Problem 60

A promissory note will pay $$\$ 27,000$$ at maturity 10 years from now. How much money should you be willing to pay now if money is worth $5.5 \%$ compounded continuously?

Kimberly Waterbury

Numerade Educator

Problem 61

In a new housing development, the houses are selling for $$\$ 100,000$$ and require a $20 \%$ down payment. The buyer is given a choice of 30-year or 15 -year financing, both at $7.68 \%$ compounded monthly.
(A) What is the monthly payment for the 30-year choice? For the 15-year choice?
(B) What is the unpaid balance after 10 years for the 30-year choice? For the 15-year choice?

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Problem 62

A loan company will loan up to $60 \%$ of the equity in a home. A family purchased their home 8 years ago for $$\$ 83,000$$. The home was financed by paying $20 \%$ down and signing a 30 -year mortgage at $8.4 \%$ for the balance. Equal monthly payments were made to amortize the loan over the 30 -year period. The market value of the house is now $$\$ 95,000$$. After making the 96th payment, the family applied to the loan company for the maximum loan. How much (to the nearest dollar) will the family receive?

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00:26

Problem 63

A $$\$ 600$$ stereo is financed for 6 months by making monthly payments of $$\$ 110$$. What is the annual nominal compounding rate for this loan?

Sheryl Ezze

Numerade Educator

05:22

Problem 64

A person deposits $$\$ 2,000$$ each year for 25 years into an IRA. When she retires immediately after making the 25 th deposit, the IRA is worth $$\$ 220,000$$.
(A) Find the interest rate earned by the IRA over the 25 -year period leading up to retirement.
(B) Assume that the IRA continues to earn the interest rate found in part (A). How long can the retiree withdraw $$\$ 30,000$$ per year? How long can she withdraw $$\$ 24,000$$ per year?

Eric Mockensturm

Numerade Educator

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