Applied Finite Mathematics by Rupinder Sekhon, UniqU, LLC - HTML preview

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Chapter 10Mathematics of Finance: Homework

SIMPLE INTEREST AND DISCOUNT

Do the following simple interest problems.

If an amount of $2,000 is borrowed at a simple interest rate of 10% for 3 years, how much is the interest?

$600
Exercise 2.

You borrow $4,500 for six months at a simple interest rate of 8%. How much is the interest?

John borrows $2400 for 3 years at 9% simple interest. How much will he owe at the end of 3 years?

$3048
Exercise 4.

Jessica takes a loan of $800 for 4 months at 12% simple interest. How much does she owe at the end of the 4-month period?

If an amount of $2,160, which includes a 10% simple interest for 2 years, is paid back, how much was borrowed 2 years earlier?

$1800
Exercise 6.

Jamie just paid off a loan of $2,544, the principal and simple interest. If he took out the loan six months ago at 12% simple interest, what was the amount borrowed?

Shanti charged $800 on her charge card and did not make a payment for six months. If there is a monthly charge of 1.5%, how much does she owe?

$872
Exercise 8.

A credit card company charges 18% interest on the unpaid balance. If you owed $2000 three months ago and have been delinquent since, how much do you owe?

An amount of $2000 is borrowed for 3 years. At the end of the three years, $2660 is paid back. What was the simple interest rate?

11%
Exercise 10.

Nancy borrowed $1,800 and paid back $1,920, four months later. What was the simple interest rate?

Jose agrees to pay $2,000 in one year at an interest rate of 12%. The bank subtracts the discount of 12% of $2,000, and gives the rest to Jose. Find the amount of the discount and the proceeds to Jose.

Discount $240, Proceeds $1760
Exercise 12.

Tasha signs a note for a discounted loan agreeing to pay $1200 in 8 months at an 18% discount rate. Determine the amount of the discount and the proceeds to her.

An amount of $8,000 is borrowed at a discount rate of 12%, find the proceeds if the length of the loan is 7 months.

$7440
Exercise 14.

An amount of $4,000 is borrowed at a discount rate of 10%, find the proceeds if the length of the loan is 180 days.

Derek needs $2400 new equipment for his shop. He can borrow this money at a discount rate of 14% for a year. Find the amount of the loan he should ask for so that his proceeds are $2400.

$2790.70
Exercise 16.

Mary owes June $750, and wants to pay her off. She decides to borrow the amount from her bank at a discount rate of 16%. If she borrows the money for 10 months, find the amount of the loan she should ask for so that her proceeds are $750?

COMPOUND INTEREST

Do the following compound interest problems involving a lump-sum amount.

If $8,000 is invested at 9.2% compounded monthly, what will the final amount be in 4 years?

$11542.52
Exercise 18.

How much should be invested at 10.3% for it to amount to $10,000 in 6 years?

Lydia's aunt Rose left her $5,000. Lydia spent $1,000 on her wardrobe and deposited the rest in an account that pays 6.9% compounded daily. How much money will she have in 5 years?

$5647.77
Exercise 20.

Thuy needs $1,850 in eight months for her college tuition. How much money should she deposit lump sum in an account paying 8.2% compounded monthly to achieve that goal?

Bank A pays 5% compounded daily, while Bank B pays 5.12% compounded monthly. Which bank pays more? Explain.

Bank B
Exercise 22.

EZ Photo Company needs five copying machines in 2 1/2 years for a total cost of $15,000. How much money should be deposited now to pay for these machines, if the interest rate is 8% compounded semiannually?

Jon's grandfather was planning to give him $12,000 in 10 years. Jon has convinced his grandfather to pay him $6,000 now, instead. If Jon invests this $6,000 at 7.5% compounded continuously, how much money will he have in 10 years?

$12702.00
Exercise 24.

What will be the price of a $20,000 car in 5 years if the inflation rate is 6%?

At an interest rate of 8% compounded continuously, how many years will it take to double your money? Hint: You may do this on your calculator by trial and error.

8.66 years
Exercise 26.

If an investment earns 10% compounded continuously, in how many years will it triple? Hint: You may do this on your calculator by trial and error.

The City Library has ordered a new computer system costing $158,000. The system will be delivered in 6 months, and the full amount will be due 30 days after delivery. How much should be deposited today into an account paying 7.5% compounded monthly to have $158,000 in 7 months?

$151257.12
Exercise 28.

Mr. and Mrs. Tran are expecting a baby girl in a few days. They want to put away money for her college education now. How much money should they deposit in an account paying 10.2% so they will have $100,000 in 18 years to pay for their daughter's educational expenses?

Find the effective interest rate for an account paying 7.2% compounded quarterly.

7.3967%
Exercise 30.

If a bank pays 5.75% compounded monthly, what is the effective interest rate?

Population of California in the year 1995 was 32 million. If the population grows at a rate of 2%, what will the population be in 2025?

57.96 million
Exercise 32.

According to the Law of 70, if an amount grows at an annual rate of 1%, then it doubles every seventy years. Suppose a bank pays 5% interest, how long will it take for you to double your money? How about at 15%?

ANNUITIES AND SINKING FUNDS

Each of the following problems involve an annuity - a sequence of payments.

Find the future value of an annuity of $200 per month for 5 years at 6% compounded monthly.

$13,954.01
Exercise 34.

How much money should be deposited at the end of each month in an account paying 7.5% for it to amount to $10,000 in 5 years?

At the end of each month Rita deposits $300 in an account that pays 5%. What will the final amount be in 4 years?

$15,904.47
Exercise 36.

Mr. Chang wants to retire in 10 years and can save $650 every three months. If the interest rate is 7.8%, how much will he have at the end of 5 years?

A firm needs to replace most of its machinery in five years at a cost of $500,000. The company wishes to create a sinking fund to have this money available in five years. How much should the quarterly deposits be if the fund earns 8%?

$20,578.36
Exercise 38.

Mrs. Brown needs $5,000 in three years. If the interest rate is 9%, how much should she save at the end of each month to have that amount in three years?

A company has a $120,000 note due in 4 years. How much should be deposited at the end of each quarter in a sinking fund to payoff the note in four years if the interest rate is 8%?

$6,438.02
Exercise 40.

You are now 20 years of age and decide to save $100 at the end of each month until you are 65. If the interest rate is 9.2%, how much money will you have when you are 65?

Is it better to receive $400 at the beginning of each month for six years, or a lump sum of $25,000 today if the interest rate is 7%? Explain.

a lump sum of $25,000
Exercise 42.

In order to save money for a new computer Jill decided to save $125 at the beginning of each month for the next 8 months. If the interest rate is 7%, how much money will she have at the end of 8 months?

Mrs. Gill puts $2200 at the end of each year in her IRA account that earns 9% per year. How much total money will she have in this account after 20 years?

$112,552.26
Exercise 44.

If the inflation rate stays at 6% per year for the next five years, how much will the price be of a $15,000 car in five years? How much must you save at the end of each month at an interest rate of 7.3% to buy that car in 5 years?

PRESENT VALUE OF AN ANNUITY AND INSTALLMENT PAYMENT

For the following problems, show all work.

Shawn has won a lottery paying him $10,000 per month for the next 20 years. He'd rather have the whole amount in one lump sum today. If the current interest rate is 8.2%, how much money can he hope to get?

$1,177,953.55
Exercise 46.

Sonya bought a car for $15,000. Find the monthly payment if the loan is to be amortized over 5 years at a rate of 10.1%.

You determine that you can afford $250 per month for a car. What is the maximum amount you can afford to pay for a car if the interest rate is 9% and you want to repay the loan in 5 years?

$12,043.34
Exercise 48.

Compute the monthly payment for a house loan of $200,000 to be financed over 30 years at an interest rate of 10%.

If the $200,000 loan in the previous problem is financed over 15 years rather than 30 years at 10%, what will the monthly payment be?

$2,149.21
Exercise 50.

Friendly Auto offers Jennifer a car for $2000 down and $300 per month for 5 years. Jason wants to buy the same car but wants to pay cash. How much must Jason pay if the interest rate is 9.4%?

The Gomez family bought a house for $175,000. They paid 20% down and amortized the rest at 11.2% over a 30-year period. Find their monthly payment.

$1,354.45
Exercise 52.

Mr. and Mrs. Wong purchased their new house for $350,000. They made a down payment of 15%, and amortized the rest over 30 years. If the interest rate is 9%, find their monthly payment.

A firm needs a piece of machinery that has a useful life of 5 years. It has an option of leasing it for $10,000 a year, or buying it for $40,000 cash. If the interest rate is 10%, which choice is better?

Leasing is better
Exercise 54.

Jackie wants to buy a $19,000 car, but she can afford to pay only $300 per month for 5 years. If the interest rate is 6%, how much does she need to put down?

Vijay's tuition at Stanford for the next year is $32,000. His parents have decided to pay the tuition by making nine monthly payments. If the interest rate is 9%, what is the monthly payment?

$3,690.22
Exercise 56.

Glen borrowed $10,000 for his college education at 8% compounded quarterly. Three years later, after graduating and finding a job, he decided to start paying off his loan. If the loan is amortized over five years at 9%, find his monthly payment for the next five years.