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Excursions in Modern Mathematics

Peter Tannenbaum

Chapter 10

Financial Mathematics - all with Video Answers

Educators

Chapter Questions

01:41

Problem 1

Express each of the following percentages as a decimal.
(a) $6.25 \%$
(b) $3 \frac{3}{4} \%$
(c) $\frac{7}{10} \%$

Shahab Ullah
Shahab Ullah
Numerade Educator
03:53

Problem 2

Express each of the following percentages as a decimal.
(a) $8.75 \%$
(b) $4 \frac{1}{8} \%$
(c) $\frac{4}{5} \%$

Lourence Gonhovi
Lourence Gonhovi
Numerade Educator
02:23

Problem 3

Express each of the following percentages as a decimal.
(a) $0.82 \%$
(b) $0.05 \%$

Shahab Ullah
Shahab Ullah
Numerade Educator
02:23

Problem 4

Express each of the following percentages as a decimal.
(a) $0.25 \%$
(b) $0.003 \%$

Shahab Ullah
Shahab Ullah
Numerade Educator
01:44

Problem 5

Suppose that your lab scores in a biology class were 61 out of 75 points in Lab 1,17 out of 20 points in Lab 2 , and 118 out of 150 in Lab 3. Compare your lab scores and rank them in order, from best to last.

Jerrah Biggerstaff
Jerrah Biggerstaff
Numerade Educator
04:56

Problem 6

There were four different sections of Financial Mathematics 101 offered last semester. In section $\mathrm{A}, 31$ out of 38 students passed the class; in section B, 47 out of 56 students passed the class; in section $\mathrm{C}, 34$ out of 45 students passed the class; and in section $\mathrm{D}, 45$ out of 52 students passed the class. Compare the passing rates in each section and rank them from best to worst.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:23

Problem 7

A 250 -piece puzzle is missing $14 \%$ of its pieces from its box. How many pieces are in the box?

Margaret Farmer
Margaret Farmer
Numerade Educator
00:45

Problem 8

Jefferson Elementary School has 750 students. The Friday before spring break $22 \%$ of the student body was absent. How many students were in school that day?

Julie Silva
Julie Silva
Numerade Educator
03:24

Problem 9

At the Happyville Mall, you buy a pair of earrings that are marked \$6.95. After sales tax, the bill was $\$ 7.61$. What is the tax rate in Happyville (to the nearest tenth of a percent)?

Ruby P
Ruby P
Numerade Educator
01:35

Problem 10

Arvin's tuition bill for last semester was $\$ 5760 .$ If he paid $\$ 6048$ in tuition this semester, what was the percentage increase on his tuition?

Rachel Lepak
Rachel Lepak
Numerade Educator
02:54

Problem 11

For three consecutive years the tuition at Tasmania State University increased by $10 \%, 15 \%,$ and $10 \%,$ respectively. What was the overall percentage increase of tuition during the three-year period?

James Kiss
James Kiss
Numerade Educator
00:33

Problem 12

For three consecutive years the cost of gasoline increased by $8 \%, 15 \%,$ and $20 \%,$ respectively. What was the overall percentage increase of the cost of gasoline during the threeyear period?

Erika Bustos
Erika Bustos
Numerade Educator
01:26

Problem 13

A shoe store marks up the price of its shoes at $120 \%$ over cost. A pair of shoes goes on sale for $20 \%$ off and then goes on the clearance rack for an additional $30 \%$ off. A customer walks in with a $10 \%$ off coupon good on all clearance items and buys the shoes. Express the store's profit on these shoes as a percentage of the original cost.

Heather Zimmers
Heather Zimmers
Numerade Educator
00:42

Problem 14

Home values in Middletown have declined $7 \%$ per year for each of the past four years. What was the total percentage decrease in home values during the four-year period? Round your answer to the nearest tenth of a percentage point.

Victor Salazar
Victor Salazar
Numerade Educator
01:18

Problem 15

Over a period of one week, the Dow Jones Industrial Average (DJIA) did the following: On Monday the DJIA went up by $2.5 \%,$ on Tuesday it went up by $12.1 \%,$ on Wednesday it went down by $4.7 \%,$ on Thursday it went up by $0.8 \%,$ and on Friday it went down by $5.4 \% .$ What was the percentage increase/decrease of the DJIA over the week? Round your answer to the nearest tenth of a percentage point.

Jeyasree R T
Jeyasree R T
Numerade Educator
01:18

Problem 16

Over a period of one week, the Dow Jones Industrial Average (DJIA) did the following: On Monday the DJIA went down by $3.2 \%,$ on Tuesday it went up by $11.2 \%,$ on Wednesday it went up by $0.7 \%,$ on Thursday it went down by $4.8 \%$ and on Friday it went down by $9.4 \% .$ What was the percentage increase/decrease of the DJIA over the week? Round your answer to the nearest tenth of a percentage point.

Jeyasree R T
Jeyasree R T
Numerade Educator
01:47

Problem 17

Suppose you borrow $\$ 875$ for a term of four years at simple interest and $4.28 \%$ APR. How much is the total (principal plus interest) you must pay back on the loan?

Monica Miller
Monica Miller
Numerade Educator
00:55

Problem 18

Suppose you borrow $\$ 1250$ for a term of three years at simple interest and $5.1 \%$ APR. How much is the total (principal plus interest) you must pay back on the loan?

Catt Huth
Catt Huth
Numerade Educator
02:36

Problem 19

Suppose you purchase a four-year bond with an APR of $5.75 \% .$ The face value of the bond is $\$ 4920 .$ Find the purchase price of the bond.

Gregory Higby
Gregory Higby
Numerade Educator
01:35

Problem 20

Suppose you purchase a 15-year U.S. savings bond with an APR of $4 \%$. The face value of the bond is $\$ 8000$. Find the purchase price of the bond.

Gregory Higby
Gregory Higby
Numerade Educator
01:25

Problem 21

Suppose you purchase an eight-year bond for $\$ 5400 .$ The face value of the bond when it matures is $\$ 8316 .$ Find the APR.

Kaylee Mcclellan
Kaylee Mcclellan
Numerade Educator
01:33

Problem 22

Suppose you purchase a six-year muni bond for $\$ 6000 .$ The face value of the bond when it matures is $\$ 7620 .$ Find the APR.

Lauren Shelton
Lauren Shelton
Numerade Educator
02:03

Problem 23

Find the APR of a bond that doubles its value in 12 years. Round your answer to the nearest hundredth of a percent.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
01:14

Problem 24

Find the APR of a bond that doubles its value in 20 years. Round your answer to the nearest hundredth of a percent.

Monica Miller
Monica Miller
Numerade Educator
02:21

Problem 25

Advance America is a payday loan company that offers quick, short-term loans using the borrower's future paychecks as collateral. Advance America charges $\$ 17$ for each $\$ 100$ loaned for a term of 14 days. Find the APR charged by Advance America.

Charles Carter
Charles Carter
Numerade Educator
01:05

Problem 26

CashNet USA is a payday loan company that offers quick, short-term loans using the borrower's future paychecks as collateral. CashNet USA charges $\$ 25$ for each $\$ 100$ loaned for a term of 14 days. Find the APR charged by CashNet USA.

Brooke Bussoletti
Brooke Bussoletti
Numerade Educator
02:36

Problem 27

Find the future value of an investment of $P=\$ 3250$ compounded annually with a $9 \%$ APR for a term of
(a) four years.
(b) five and a half years.

Gregory Higby
Gregory Higby
Numerade Educator
02:36

Problem 28

Find the future value of an investment of $P=\$ 1237.50$ compounded annually with a $8.25 \%$ APR for a term of
(a) three years.
(b) four and a half years.

Gregory Higby
Gregory Higby
Numerade Educator
01:37

Problem 29

Between 1990 and 2010 the average annual inflation rate was $3.5 \%$. Find the salary in 2010 dollars that would be equivalent to a $\$ 25,000$ salary in 1990 .

Ashly Sunny
Ashly Sunny
Numerade Educator
01:33

Problem 30

Between 2000 and 2011 the average annual inflation rate was $3 \%$. Find the salary in 2000 dollars that would be equivalent to a $\$ 50,000$ salary in 2011 .

Carson Merrill
Carson Merrill
Numerade Educator
04:13

Problem 31

Consider a CD paying a $3 \%$ APR compounded monthly.
(a) Find the periodic interest rate.
(b) Find the future value of the $\mathrm{CD}$ if you invest $\$ 1580$ for a term of three years.

Nick Johnson
Nick Johnson
Numerade Educator
02:24

Problem 32

Consider a CD paying a 3.6\% APR compounded monthly.
(a) Find the periodic interest rate.
(b) Find the future value of the $\mathrm{CD}$ if you invest $\$ 3250$ for a term of four years.

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
04:13

Problem 33

Consider a CD paying a $3.65 \%$ APR compounded daily.
(a) Find the periodic interest rate.
(b) Find the future value of the $\mathrm{CD}$ if you invest $\$ 1580$ for a term of three years.

Nick Johnson
Nick Johnson
Numerade Educator
02:24

Problem 34

Consider a CD paying a $4.38 \%$ APR compounded daily.
(a) Find the periodic interest rate.
(b) Find the future value of the $\mathrm{CD}$ if you invest $\$ 3250$ for a term of four years.

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
02:36

Problem 35

Consider a CD paying a $3 \%$ APR compounded continuously. Find the future value of the $\mathrm{CD}$ if you invest $\$ 1580$ for a term of three years.

Gregory Higby
Gregory Higby
Numerade Educator
01:39

Problem 36

Consider a CD paying a $3.6 \%$ APR compounded continuously. Find the future value of the $\mathrm{CD}$ if you invest $\$ 3250$ for a term of four years.

Amy Jiang
Amy Jiang
Numerade Educator
02:36

Problem 37

Consider a CD paying a $3.65 \%$ APR compounded continuously. Find the future value of the CD if you invest $\$ 1580$ for a term of 500 days. Round your answer to the nearest dollar.

Gregory Higby
Gregory Higby
Numerade Educator
02:18

Problem 38

Consider a CD paying a $3.6 \%$ APR compounded continuously. Find the future value of the CD if you invest $\$ 3250$ for a term of 1000 days. Round your answer to the nearest dollar.

Nick Johnson
Nick Johnson
Numerade Educator
02:04

Problem 39

Suppose you invest $\$ P$ on a CD paying $2.75 \%$ interest compounded continuously for a term of three years. At the end of the term you get $\$ 868.80$ from the bank. Find the value of the original principal $P$.

Anjali Kurse
Anjali Kurse
Numerade Educator
02:09

Problem 40

Suppose you invest $\$ P$ on a CD paying $1.85 \%$ interest compounded continuously for a term of five years. At the end of the term you get $\$ 1645.37$ from the bank. Find the value of the original principal $P$.

Audrey Fong
Audrey Fong
Numerade Educator
01:06

Problem 41

Find the APY for an APR of $6 \%$ compounded
(a) yearly.
(b) semi-annually.
(c) monthly.
(d) continuously.

Catt Huth
Catt Huth
Numerade Educator
03:29

Problem 42

Find the APY for an APR of $3.6 \%$ compounded
(a) yearly.
(b) semi-annually.
(c) monthly.
(d) continuously.

Gregory Higby
Gregory Higby
Numerade Educator
02:21

Problem 43

For an investment having an APY of $6 \%$, estimate the number of years needed to double the principal.

Emily Frampton
Emily Frampton
Numerade Educator
02:41

Problem 44

For an investment having an APY of $7.2 \%$, estimate the number of years needed to double the principal.

SS
Stephanie Schwartz
Numerade Educator
03:36

Problem 45

Find the value of a retirement savings account paying an APR of $6.6 \%$ after 45 years (contributions made at the end of each year, including the last year) when the annual contribution is
(a) $\$ 1500$
(b) $\$ 750$
(c) $\$ 2250$

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
02:24

Problem 46

Find the value of a retirement savings account paying an APR of $5.4 \%$ after 40 years (contributions made at the end of each year, including the last year) when the annual contribution is
(a) $\$ 1200$
(b) $\$ 600$
(c) $\$ 1800$

Tony Ni
Tony Ni
Numerade Educator
03:36

Problem 47

Find the value of a retirement savings account with an annual contribution of $\$ 1500$ (contributions made at the end of each year, including the last year), and an APR of $6.6 \%$ after
(a) 40 years.
(b) 50 years.
(c) 52 years.

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
02:04

Problem 48

Find the value of a retirement savings account with an annual contribution of $\$ 1200$ (contributions made at the end of each year, including the last year), and an APR of $5.4 \%$ after
(a) 35 years.
(b) 45 years.
(c) 50 years.

AG
Ankit Gupta
Numerade Educator
02:18

Problem 49

Find the value of a retirement savings account paying an APR of $6.6 \%$ (compounded monthly) after 45 years of monthly contributions (contributions made at the end of each month, including the last month) when the monthly contribution is
(a) $\$ 125$
(b) $\$ 62.50$
(c) $\$ 187.50$

Nick Johnson
Nick Johnson
Numerade Educator
02:01

Problem 50

Find the value of a retirement savings account paying an APR of $5.4 \%$ (compounded monthly) after 40 years of monthly contributions (contributions made at the end of each month, including the last month) when the monthly contribution is
(a) $\$ 100$
(b) $\$ 50$
(c) $\$ 150$

Julie Silva
Julie Silva
Numerade Educator
02:54

Problem 51

Find the value of a retirement savings account with a monthly contribution of $\$ 125$ (contributions made at the end of each month, including the last month) and an APR of $6.6 \%$ (compounded monthly) after
(a) 40 years.
(b) 50 years.
(c) $521 / 2$ years.
[Note: You may want to compare your answers to each other and to your answer to Exercise $49(\mathrm{a})$.

Angela Guo
Angela Guo
Numerade Educator
02:54

Problem 52

Find the value of a retirement savings account with a monthly contribution of $\$ 100$ (contributions made at the end of each month, including the last month) and an APR of $5.4 \%$ (compounded monthly) after
(a) 35 years.
(b) 45 years.
(c) $491 / 2$ years.
[Note: You may want to compare your answers to each other and to your answer to Exercise $50(\mathrm{a}) .]$

Angela Guo
Angela Guo
Numerade Educator
03:08

Problem 53

What should your monthly contribution be if your goal is to have $\$ 500,000$ in your retirement savings account after 40 years? Assume the APR is $6.6 \%$ compounded monthly and that contributions are made at the end of each month, including the last month.

AG
Ankit Gupta
Numerade Educator
03:08

Problem 54

What should your monthly contribution be if your goal is to have $\$ 400,000$ in your retirement savings account after 50 years? Assume the APR is $5.4 \%$ compounded monthly and that contributions are made at the end of each month, including the last month.

AG
Ankit Gupta
Numerade Educator
05:22

Problem 55

Consider a retirement savings account where the monthly contribution is $\$ 125$ for the first 20 years, is increased to $\$ 225$ for the next 15 years, and then is increased once again to $\$ 400$ for the last 5 years. The APR is always $6.6 \%$ compounded monthly. What is the value of the account at the end of 40 years?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
01:33

Problem 56

Consider a retirement savings account where the monthly contribution is $\$ 100$ for the first 20 years, is increased to $\$ 225$ for the next 15 years, and then is increased once again to $\$ 425$ for the last 10 years. The APR is always $5.4 \%$ compounded monthly. What is the value of the account at the end of 45 years?

Lourence Gonhovi
Lourence Gonhovi
Numerade Educator
02:22

Problem 57

Suppose you purchase a car and you are going to finance $\$ 14,500$ for 36 months at an APR of $6 \%$ compounded monthly. Find the monthly payments on the loan.

Suzana Milea
Suzana Milea
Numerade Educator
03:19

Problem 58

Suppose you purchase a car and you are going to finance $\$ 18,700$ for 60 months at an APR of $4.8 \%$ compounded monthly. Find the monthly payments on the loan.

Oluwadamilola Ameobi
Oluwadamilola Ameobi
Numerade Educator
03:39

Problem 59

Suppose you want to buy a car. The dealer offers a financing package consisting of a $3.6 \%$ APR compounded monthly for a term of four years. Suppose that you want your monthly payments to be at most $\$ 400 .$ What is the maximum amount that you should finance? (Round your answer to the nearest dollar.)

Kayla Laughman
Kayla Laughman
Numerade Educator
02:08

Problem 60

Suppose you want to buy a car. The dealer offers a financing package consisting of a $6 \%$ APR compounded monthly for a term of five years. Suppose that you want your monthly payments to be at most $\$ 320 .$ What is the maximum amount that you should finance? Give your answer to the nearest dollar.

Nick Johnson
Nick Johnson
Numerade Educator
02:06

Problem 61

The Simpsons are planning to purchase a new home. To do so, they will need to take out a 30-year home mortgage loan of $\$ 160,000$ through Middletown Bank. Annual interest rates for 30-year mortgages at Middletown Bank are $5.75 \%$ compounded monthly.
(a) Compute the Simpsons' monthly mortgage payment under this loan.
(b) How much interest will the Simpsons pay over the life of the loan?

Sam Limsuwannarot
Sam Limsuwannarot
Numerade Educator
01:29

Problem 62

The Smiths are refinancing their home mortgage to a $15-$ year loan at $5.25 \%$ annual interest compounded monthly. Their outstanding balance on the loan is $\$ 95,000$
(a) Under their current loan, the Smiths' monthly mortgage payment is $\$ 1104 .$ How much will the Smiths be saving in their monthly mortgage payments by refinancing? (Round your answer to the nearest dollar.)
(b) How much interest will the Smiths pay over the life of the new loan?

Zach Steedman
Zach Steedman
Numerade Educator
01:29

Problem 63

Ken just bought a house. He made a $\$ 25,000$ down payment and financed the balance with a 20-year home mortgage loan with an interest rate of $5.5 \%$ compounded monthly. His monthly mortgage payment is $\$ 950 .$ What was the selling price of the house?

Xiaomeng Zhang
Xiaomeng Zhang
Numerade Educator
01:36

Problem 64

Cari just bought a house. She made a $\$ 35,000$ down payment and financed the balance with a 30 -year home mortgage loan with an interest rate of $5.75 \%$ compounded monthly. Her monthly mortgage payment is $\$ 877 .$ What was the selling price of the house?

Aamir Mithaiwala
Aamir Mithaiwala
Numerade Educator
06:34

Problem 65

Elizabeth went on a fabulous vacation in May and racked up a lot of charges on her credit card. When it came time to pay her June credit card bill, she left a balance of $\$ 1200$. Elizabeth's credit card billing cycle runs from the nineteenth of each month to the eighteenth of the next month, and her interest rate is $19.5 \% .$ She started the billing cycle June $19-$ July 18 with a previous balance of $\$ 1200 .$ In addition, she made three purchases, with the dates and amounts shown in Table 10-11. On July 15 she made an online payment of $\$ 500.00$ that was credited to her balance the same day.
(a) Find the average daily balance on the credit card account for the billing cycle June 19 -July 18 .
(b) Compute the interest charged for the billing cycle June 19-July 18 .
(c) Find the new balance on the account at the end of the June 19 -July 18 billing cycle.
$$
\begin{array}{|c|c}
\hline \text { Date } & \text { Amount of purchase/payment } \\
\hline 6 / 21 & \$ 179.58 \\
\hline 6 / 30 & \$ 40.00 \\
\hline 7 / 5 & \$ 98.35 \\
\hline 7 / 15 & \text { Payment } \$ 500.00
\end{array}
$$

Stephen Hobbs
Stephen Hobbs
Numerade Educator
03:35

Problem 66

Reid's credit card cycle ends on the twenty-fifth of every month. The interest rate on Reid's Visa card is $21.99 \%,$ and the billing cycle runs from the twenty-sixth of a month to the twenty-fifth of the following month. At the end of the July 26-Aug. 25 billing cycle, Reid's balance was $\$ 5000$. During the next billing cycle (Aug. 26-Sept. 25) Reid made three purchases, with the dates and amounts shown in Table $10-12 .$ On September 22 Reid made an online payment of $\$ 200$ that was credited towards his balance the same day.
(a) Find the average daily balance on the credit card account for the billing cycle Aug. 26-Sept. $25 .$
(b) Find the interest charged for the billing cycle Aug. 26 Sept. $25 .$
(c) Find the new balance on the account at the end of the Aug. 26-Sept. 25 billing cycle.
$$
\begin{array}{|l|c|}
\hline \text { Date of purchase } & \text { Amount of purchase } \\
\hline 8 / 31 & \$ 148.55 \\
\hline 9 / 12 & \$ 30.00 \\
\hline 9 / 19 & \$ 103.99 \\
\hline
\end{array}
$$

Cory Kuzinski
Cory Kuzinski
Numerade Educator
01:26

Problem 67

How much should a retailer mark up her goods so that when she has a $25 \%$ off sale, the resulting prices will still reflect a $50 \%$ markup (on her cost)?

Heather Zimmers
Heather Zimmers
Numerade Educator
03:13

Problem 68

Joe, a math major, calculates that in the last three years tuition at Tasmania State University has increased a total of exactly $12.4864 \% .$ He also knows that tuition increased by the same percentage each year. Determine this percentage.

Tommy Nguyen
Tommy Nguyen
Numerade Educator
02:21

Problem 69

You have a coupon worth $x \%$ off any item (including sale items) in a store. The particular item you want is on sale at $y \%$ off the marked price of $\$ P .$ (Assume that both $x$ and $y$ are positive integers smaller than $100 .)$
(a) Give an expression for the price of the item assuming that you first got the $y \%$ off sale price and then had the additional $x \%$ taken off using your coupon.
(b) Give an expression for the price of the item assuming that you first got the $x \%$ off the original price using your coupon and then had the $y \%$ taken off from the sale.
(c) Explain why it makes no difference in which order you have the discounts taken.

Melissa Munoz
Melissa Munoz
Numerade Educator
01:33

Problem 70

You buy a $\$ 500$ certificate of deposit $(\mathrm{CD}),$ and at the end of two years you cash it for $\$ 561.80 .$ What is the annual yield of this investment?

Carson Merrill
Carson Merrill
Numerade Educator
08:38

Problem 71

You are purchasing a home for $\$ 120,000$ and are shopping for a loan. You have a total of $\$ 31,000$ to put down, including the closing costs of $\$ 1000$ and any loan fee that might be charged. Bank $A$ offers a $10 \%$ APR amortized over 30 years with 360 equal monthly payments. There is no loan fee. Bank $B$ offers a $9.5 \%$ APR amortized over 30 years with 360 equal monthly payments. There is a $3 \%$ loan fee (i.e., a one-time up-front charge of $3 \%$ of the loan). Which loan is better?

Jason Orozco
Jason Orozco
Numerade Educator
04:51

Problem 72

You want to purchase a new car. The price of the car is $\$ 24,035 .$ The dealer is currently offering a special promotion: (1) You can choose a $\$ 1500$ rebate up front and finance the balance at $6 \%$ for 60 months, or (2) $0 \%$ financing for the first 36 months and $6 \%$ financing for the remaining 24 months of your loan. Which is the better deal? Justify your answer by computing your monthly payments over 60 months under each of the two options.

Christopher Stanley
Christopher Stanley
Numerade Educator
06:13

Problem 73

According to a Philadelphia Inquirer finance column, "Borrow $\$ 100,000$ with a $6 \%$ fixed-rate mortgage and you'll pay nearly $\$ 116,000$ in interest over 30 years. Put an extra $\$ 100$ a month into principal payments and you'd pay just $\$ 76,000-$ and be done with mortgage payments nine years earlier." (“Are Extra Mortgage Payments Good Idea?" in Philadelphia Inquirer. Copyright @ 2012 by Philadelphia Inquirer. Used by permission of Philadelphia Inquirer.)
(a) Verify that the increase in the monthly payment that is needed to pay off the mortgage in 21 years is indeed close to $\$ 100$ and that roughly $\$ 40,000$ will be saved in interest.
(b) How much should the monthly payment be increased so as to pay off the mortgage in 15 years? How much interest is saved in doing so?
(c) How much should the monthly payment be increased so as to pay off the mortgage in $t$ years $(t<30) ?$ Express the answer in terms of $t$

AG
Ankit Gupta
Numerade Educator
02:47

Problem 74

Investor A invests $P$ for $t$ years in a savings account with an APR $r$ compounded continuously. Investor $\mathrm{B}$ invests the same principal $P$ for twice as long $(2 t$ years $)$ in a savings account with an APR that is half as much $(r / 2)$, also compounded continuously. When all is said and done, which of the two investors ends up with more money? Explain your answer.

Heather Zimmers
Heather Zimmers
Numerade Educator
03:08

Problem 75

[In all the retirement savings accounts, assume that the frequency of contributions (annual or monthly), the term, and the APR all remain the same.]
(a) Explain why, in the retirement savings formula (be it the annual or the monthly version), the value $V$ of the account is proportional to the contribution $P$. In other words, explain why if a contribution of $P$ generates an account with value $V,$ then a contribution of $c P$ (where $c$ is any positive constant) generates an account with value $c V$. (Hint: What happens in the retirement savings formula when you replace $P$ by $c P ?$ )
(b) Explain why if a contribution of $P$ generates a retirement savings account with value $V,$ and a contribution of $Q$ generates a retirement savings account with value $W,$ then a contribution of $(P+Q)$ generates a retirement savings account with value $(V+W)$.

AG
Ankit Gupta
Numerade Educator
02:10

Problem 76

[In all the installment loans, assume that the term of the loan and the APR remain the same.]
(a) Explain why, in the amortization formula, the monthly payment $M$ is proportional to the principal $P$. In other words, explain why if the monthly payment on a loan with principal $P$ is $M,$ then the monthly payment on a loan with principal $c P$ (where $c$ is any positive constant) is $c M$. (Hint: What happens in the amortization formula when you replace $P$ by $c P ?)$
(b) Explain why if the monthly payment on a loan with principal $P$ is $M,$ and the monthly payment on a second loan with principal $Q$ is $N,$ then the monthly payment on a loan with principal $(P+Q)$ is $(M+N)$.

Ahmad Reda
Ahmad Reda
Numerade Educator