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MATH 106 6383 Finite Mathematics (2192)
Week 1 Discussion
LEO Participation Discussion Topics
SIMPLE INTEREST AND DISCOUNT
1.            You borrow \$4,500 for six months at a simple interest rate of 8%. How much is the interest?
2.            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?
3.            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?
4.            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?
5.            Nancy borrowed \$1,800 and paid back \$1,920, four months later. What was the simple interest rate?
6.            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.
7.            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.
8.            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
9.            How much should be invested at 10.3% for it to amount to \$10,000 in 6 years?
10.          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?
11.          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?
12.          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?
13.          What will be the price of a \$20,000 car in 5 years if the inflation rate is 6%?
14.          Bank A pays 5% compounded daily, while Bank B pays 5.12% compounded monthly. Which bank pays more? Explain.
15.          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?
16.          If a bank pays 5.75% compounded monthly, what is the effective interest rate?
ANNUITIES AND SINKING FUNDS
17.          How much money should be deposited at the end of each month in an account paying 7.5% compounded monthly for it to amount to \$10,000 in 5 years?
18.          Find the future value of an annuity of \$200 per month for 5 years at 6% compounded monthly.
19.          At the end of each month Rita deposits \$300 in an account that pays 5% compounded monthly. What will the final amount be in 4 years?
20.          Mr. Chang wants to retire in 10 years and can save \$650 every three months. If the interest rate is 7.8% compounded quarterly, how much will he have at the end of 5 years?
21.          Mrs. Brown needs \$5,000 in three years. If the interest rate is 9% compounded monthly, how much should she save at the end of each month to have that amount in three years?
22.          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% compounded monthly, how much money will you have when you are 65?
23.          In order to save money for a new computer Jill decided to save \$125 at the end of each month for the next 8 months. If the interest rate is 7% compounded monthly, how much money will she have at the end of 8 months?
24.          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% compounded monthly to buy that car in 5 years?
PRESENT VALUE OF AN ANNUITY AND INSTALLMENT PAYMENT
25.          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%.
26.          Compute the monthly payment for a house loan of \$200,000 to be financed over 30 years at an interest rate of 10%.
27.          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%?
28.          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.
29.          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.
30.          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?
31.          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.
MISCELLANEOUS APPLICATION PROBLEMS
32.          A \$200,000 house loan is amortized over 30 years at an interest rate of 10.4%.
a.            Find the monthly payment.
b.            Find the balance owed after 20 years.
c.             Find the balance of the loan after 100 payments.
d.            Find the monthly payment if the original loan were amortized over 15 years.
33.          Mr. Smith is planning to retire in 25 years and would like to have \$250,000 then. What monthly payment made at the end of each month to an account that pays 6.5% compounded monthly will achieve his objective?
34.          You have a choice of either receiving \$5,000 at the end of each year for the next 5 years or receiving \$3000 per year for the next 10 years. If the current interest rate is 9% compounded annually, which is better?
35.          Find the fair market value of the ten-year \$1,000 bond that pays \$35 every six months, if the current interest rate has dropped to 6% compounded semi-annually.
Hint: You must do the following.
a.            Find the present value of \$1000.
b.            Find the present value of the \$35 payments.
c.             The fair market value of the bond=a+b

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