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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…