Business Mathematics Final Assignment -
1. A small computer desk cost a retailer $185.00 and the accompanying chair cost $43.00. In a special sale, the retailer offers the chair "free" to customers who purchase the desk. Find the selling price of the desk if the retailer prices it so that he will still the equivalent of a 12% markup rate based on the cost of both items.
2. A store has a special sale in which a few loss leader items are sold at cost in order to attract customers. During one day of the sale, the store sold $1,864.00 at cost and $14,587.00 at the regular selling price. Find the cost of all items sold if the total sale that day had an average markup rate on cost of 20%.
3. Tony Frasier works at men's clothing store. The store's cost for a shipment of 12 dozen t-shirts is $1,044.00. If Tony sells 65 of the shirts for $15.00 each, then reduces the selling price to $11.95 and sells 60 more, and finally sells the remaining 19 t-shirts at a close-out sale price of $7.95 each, what is the store's average markup rate on cost for these shirts?
4. A mail-order catalog has automotive shock absorbers for $48.99 a pair plus a shipping charge of $2.69. A local store has a special sale with 25% off the list price of $63.99. Which is the better bargain?
5. A women's clothing store is having a clearance sale on spring merchandise. All spring items are reduced by 33.33% for one week. Furthermore, every item which doesn't sell during the first week sale will be reduced 25% off the sale price. A dress with a list price of $48.95 went through both price reductions. What is the sale price after the second reduction and what is the corresponding discount rate based on the original list price?
6. Find the simple interest on a deposit of $700.00 for 90 days at 2.75%. (Assume a non leap year)
7. Find the simple interest on a deposit of $250.00 for 283 days at 15%. (Assume a non leap year)
8. Find the simple interest on a deposit of $100.00 for 180 days at 5%. (Assume a leap year)
9. Find the simple interest on a deposit of $1000.00 for 45 days at 6%. (Assume a leap year)
10. Find the number of days in the interest period from May 24, 1992 to July 3, 1992.
11. Find the simple interest on $200.00 from July 31, 1981 to October 25, 1981 at 11.5%.
12. Find the annual percentage rate for $75.00 simple interest on $1200.00 for one year. Round your answer to the nearest hundredth of a percent and assume it is a non leap year.
13. Find the annual percentage rate for $11.56 simple interest on $1250.00 for 90 days. Round your answer to the nearest hundredth of a percent and assume it is a leap year.
14. Find the annual effective yield for a savings account that accumulated $110.00 interest on $2500.00. Assume that the interest period is one year.
15. Find the annual effective yield after taxes for the savings plan in exercise 14. Assume that the interest is being earned by a person in a 30% tax bracket and that this plan is not tax-exempt.
16. $5000.00 deposited in a savings account paying 6% compounded quarterly.
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Quarter
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Principal
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Interest
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Balance
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1
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$500.00
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2
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3
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4
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Annual Effective Yield:
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17. Complete the following table for a deposit of $5000.00 at 6% for one year.
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1
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4
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12
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365
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Continuously
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Number of compoundings per year
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Balance after
one year
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Annual effective tield
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18. Complete the following table for a deposit of $10,000.00 at 4.5% for ten years.
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1
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4
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12
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365
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Continuously
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Number of compoundings per year
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Balance after two years
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In Exercises 19 and 20, use the table from exercise 17 to find the amount for each savings plan.
19. $2000.00 at 6% compounded monthly for eight years.
20. $500.00 at 5% compounded continuously for four years.
21. Dorothy Newmeyer has a passbook savings account that pays 6% compounded daily. Her balance on January 1 is $3162.47. During that year, she deposited $422.50 on February 16, $150.00 on August 28, and withdrew $1250.00 on July 14. (Assume a non-leap year)
- What is Dorothy's balance on January 1 of the following year?
- How much interest did Dorothy's account earn during the year?
22. Joyce Oakley wants to set aside an amount now so that there will be $5000.00 available for her daughter to start college in ten years. What amount should she invest now at 8% compounded daily? (Hint: Solve for P in the given formula)
A = P (1 + R/365) AN
23. Beverley Jordan deposits $500.00 into her daughter's savings account twice a year (January 1 and July 1) for five years. The account earns 6% compounded semi-annually. Complete the following annuity table for Beverly's daughter's savings plan.
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Deposit Number
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Deposit
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Principal
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Interest
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Balance
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1
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$500.00
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2
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3
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4
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5
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6
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7
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8
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9
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10
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24. Kim and Larry Palmer decide to deposit $40.00 a month in a savings account for their son Daniel. If the account earns 6% compounded monthly, what is the balance in Daniel's account after 15 years?
25. Sam Spiegel wants to accumulate $25,000.00 in five years. How much should Sam deposit each month in an increasing annuity paying 4.5% compounded monthly?
26. Carolyn North's father deposited $43,899.77 in a decreasing annuity on January 2, 1996. Carolyn planned to begin a five-year medical volunteer program in January 1997. At that time, Carolyn will begin drawing $10,000.00 per year for five years. Complete the following decreasing annuity table assuming the account pays 4.5% annually.
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Date
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Principal
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Interest
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Balance before withdrawal
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Withdrawal
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Balance after withdrawal
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2/1/2012
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$43,899.77
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$43,899.77
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$43,899.77
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2/1/2013
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$43,899.77
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$10,000.00
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2/1/2014
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$10,000.00
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2/1/2015
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$10,000.00
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2/1/2016
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$10,000.00
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2/1/2017
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$10,000.00
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In Exercise 27 find a) the initial deposit (present value), b) the total amount withdrawn, and c) the total interest.
27. A decreasing annuity paying $500.00 per month for two years at 5.5% compounded monthly.
In Exercise 28 find the amount of each period withdrawal.
28. Monthly withdrawals from a $50,000.00 decreasing annuity at 7.5% compounded monthly over a period of a) five years, b) ten years, c) twenty years.
29. Christine Sutton wishes to set up a retirement plan to supplement her social security retirement benefits. To do this, Christine makes monthly payments into an increasing annuity, which at age 62 will begin paying her $1000.00 per month for 20 years. If the annuity pays 7.75% compounded monthly and Christine is 40 years old, how much should she set aside each month? (Assume that Christine has 22 full years in which to make payments).
30. Ralph Holzer purchases a mountain bike for $489.00 plus a 6% sales tax. He pays $75.00 down and finances the remainder of the cost.
- Determine the amount of sales tax.
- Determine the loan proceeds.
31. For the purchase from exercise 30, suppose that Ralph signed a 90-day promissory note.
- Determine the "other" charges if Ralph was required to pay an insurance premium equal to 2% of the loan proceeds.
- Add the result of the previous part to the loan proceeds to determine the amount financed.
- Determine the finance charge if the interest rate is 12% (annual percentage rate) of the amount financed.
- Use the results of the first and third parts to find the cost of Ralph's loan.
32. A loan of $2000.00 taken out on June 1, 1995 for 9 months at an annual percentage rate of 12%. (Recall that 1996 is a leap year). Find the total amount due of the loan.
33. A bank lends $500.00 to Carlo Abernathy for one year at 12% interest (discounted rate).
- Find the finance charge for this loan.
- What is the annual percentage rate for this loan?
34. Mary Simmons borrows $10,000.00 for 90 days at 10% annual interest (Banker's rule). What is the finance charge for this loan and what is the actual annual percentage rate?
In exercise 35 find the: a) the monthly payment, b) the total payment, and c) the finance charge.
35. An installment loan for $1500.00 to be repaid in 12 monthly payments with an annual percentage rate of 20%.
36. The Austins are buying a sofa by financing $900.00 on an installment plan in which the annual percentage rate is 16%. They have a choice of repaying in 12 monthly installments or 18 monthly installments.
- What is the monthly payment for each plan?
- What is the finance charge for each plan?
- What is one advantage of each plan?
37. Benjamin Scott buys a lawn and garden tractor and decides to borrow $1200.00 at an annual percentage rate of 10.5% to be repaid in nine monthly installments. Construct an amortization schedule for this loan.
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Payment Number
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Balance before Payment
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Payment
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Interest Payment
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Principal Payment
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Balance after Payment
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7
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8
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9
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