Download Discrete Math Review, Chapter 8

Discrete Math Review, Chapter 8
1. Express 18 as a percent. 12.5%
3. Express 3% as a decimal. 0.03
Name ______________________________________
2. Express 0.72 as a percent. 72%
4. What is 8% of 120? 9.6
5. Suppose the local sales tax rate is 6% and you purchase a backpack for $24.00
a. How much tax is paid? $1.44
b. What is the backpack’s total cost? $25.44
6. A television is priced at $850 and is on sale at 35% off.
a. What is the amount of the discount? $297.50 b. What is the sale price of the television? $552.50
7. A dictionary regularly sells for $56. The sale price is $36.40. What is the percent decrease of the sale price from
the regular price? 35%
8. Find the simple interest if the principal is $8,400 at 5% interest for 6 years. $2,520
9. Find the simple interest if the principal is $36,000, the interest rate is 15%, and the time is 60 days. $900
10. John borrowed $5,000 from a bank. He paid back a total of $5,750 over a 2 year period. Find the SIMPLE
interest rate. 15%
11. You plan to purchase a sailboat in four years at a cost of $12,500. How much should you invest now, at 7.3%
simple interest, to have enough to purchase the boat in four years? $9,674.92
12. Find the effective interest rate on a loan at 7.25% interest compounded…
a. semi-annually 7.38% b. quarterly 7.45% c. monthly 7.50%
The principal represents an amount of money deposited in a savings account that provides the lender
compound interest at the given rate. For questions 13 and 14: A. Determine the amount of money that
will be in the account after the given number of years. B. Find the interest earned.
13. Principal = $30,000, interest rate = 2.5% compounded quarterly for 10 years. $38,490.80 / $8,490.80
14. Principal = $2,500, interest rate = 4% compounded monthly for 20 years. $5,556.46 / $3,056.46
15. Suppose you have $14,000 to invest. Which investment yields the greater return over 10 years: 7%
compounded monthly or 6.85% compounded continuously? How much more is yielded by the better
investment? monthly --- $362.45
16. How much money should be deposited into an account that earns 7% interest compounded monthly so that the
account will accumulate $100,000 in 18 years? $28,469.43
17. $2,000 is invested into an account that pays 6% interest compounded quarterly. Find the future value of the
investment after 1 year, to the nearest cent. $2,122.73
18. You spend $10 per week on lottery tickets, averaging $520 per year. Instead of buying lottery tickets, if you
deposited the $520 at the end of each year into an annuity paying 6% compounded annually…
A. How much would you have in 20 years?
B. Find the interest earned over the 20 years.
$19,128.51
$8,728.51
19. To save for retirement, you decide to deposit $100 at the end of each month into an IRA that pays 5.5%
compounded monthly.
A. How much will your IRA have after 30 years?
B. Find the interest earned.
$91,361.19
$55,361.19
20. You would like to have $25,000 to use as a down payment for a home in five years by making regular deposits
at the end of every three months in an annuity that pays 7.25% compounded quarterly.
A. Determine the amount of each deposit, rounded to the nearest dollar. $1,048
B. How much of the $25,000 comes from deposits and how much comes from interest? $4,040
21. The price of a home that you have agreed to purchase is $240,000. The bank requires a 20% down payment
and two points at the time of closing. The cost of the home is financed with a 30 year fixed-rate mortgage at 7%.
A. Find the required down payment. $48,000
B. Find the amount of mortgage. $192,000
C. Determine how much must be paid for the two points at closing. $3,840
D. Find the monthly payment, rounded to the nearest dollar amount. $1,277
E. Find the total cost of interest over 30 years. $267,720
22. You need a loan of $100,000 to purchase a home. There are 2 options available to you:
Option A: 30-year fixed-rate at 8.5% with no closing costs and no points.
Option B: 30-year fixed-rate at 6.5% with $1,300 closing costs and 3 points.
A. Determine your monthly payments for each option, rounded to the nearest dollar. $769 / $632
B. Which option has the greater overall cost, and by how much? option A by $45,020
23. You decide to buy a new car, which costs $15,000. You can select one of the following options on a loan, each
requiring regular monthly payments.
Option A: a 3-year loan at 7.2% APR.
Option B: a 5-year loan at 8.1% APR.
A. Find the monthly payments, rounded to the nearest cent, and the total interest for option A.
$464.53 / $1,723.08
B. Find the monthly payments, rounded to the nearest cent, and the total interest for option B.
$304.86 / $3,291.60
C. Compare the monthly payments and the interest paid for each option. Discuss why someone would
choose option A why someone would choose option B.
Answers vary…