Business Mathematics Assignment -
1. Jack Hilbert invests $1000.00 at the beginning of each year for five years. The account earns 5% compounded annually. Complete the following annuity table for Jack's saving 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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$1000.00
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2
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3
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4
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5
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In Exercises 2 and 3, find the balance of each increasing annuity (using the balance formula).
2. A periodic, annual deposit of $2000.00 at 12% compounded annually for 15 years.
3. A periodic weekly deposit of $40.00 at 6% compounded weekly for five years.
4. Maria Keller made deposits of $200.00 at the beginning of each month for four years. The account earns 7% compounded monthly. After four years of deposits, Maria leaves the money in the account for an additional six years (without making any further deposits). Find the balance in Maria's account at the end of the ten years. (Hint: Use the annuity formula first, then apply the compound interest formula to annuity balance)
5. Sherrie Orlov wants to save $1000.00 in one year by making weekly deposits into a savings account that pays 3.5% compounded weekly.
- How much should Sherrie deposit into her account each week?
- At the end of the year, Sherrie purchases a $1000.00 four-year savings certificate paying 5% compounded daily. How much will the certificate be worth at maturity?
6. Robert Simpson inherited a large sum from his grandparents' estate. Part of this inheritance was placed in a decreasing annuity that will pay Robert $2500.00 per month for 25 years. If the annuity pays 5% compounded monthly and the initial deposit was $427,650.09, complete the following table showing the first six withdrawals. Over the period of 25 years, how much will Robert withdraw from this account? (Assume the initial deposit was made on May 1, 1995).
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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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1/5/2015
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$427,650.09
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$427,650.09
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$427,650.09
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1/6/2015
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$427,650.09
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$2,500.00
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1/7/2015
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$2,500.00
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1/8/2015
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$2,500.00
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1/9/2015
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$2,500.00
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1/10/2015
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$2,500.00
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1/11/2015
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$2,500.00
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In Exercise 7 find a) the initial deposit (present value), b) the total amount withdrawn, and c) the total interest.
7. A decreasing annuity paying $10,000.00 per year for ten years at 3.25% compounded annually.
In Exercise 8 find the amount of each period withdrawal.
8. Quarterly withdrawals from a $10,000.00 decreasing annuity at 6% compounded quarterly over a period of a) two years, b) five years, c) ten years.
The annuity table from your notes gives the monthly deposit (in an increasing annuity) required to build a decreasing annuity paying $1000.00 per month for 20 years. In exercises 9 and 10 find a) the monthly deposit, b) the total deposit, and c) the total interest earned by the time the account is closed.
9. Monthly deposits for 15 years at 7.5% compounded monthly.
10. Monthly deposits for 30 years at 5.5% compounded monthly.
11. Fill in the blanks in the following table. (Note: 2012 is a leap year)
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Date of Loan
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Term
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Date Due
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July 19, 2011
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3 months
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July 19, 2011
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90 days
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6 months
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November 20, 2012
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180 days
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November 20, 2012
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January 13, 2011
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July 13,2012
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January 13, 2012
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April 12, 2012
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In exercises 12 and 13 find the total amount due on each loan.
12. A loan of $800.00 for 90 days at an annual percentage rate of 18%.
13. A loan of $800.00 for 3 months at an annual percentage rate of 18%. (Assume the loan is taken out on June 1)
14. Bill and Carly Taylor took out a 90-day note for $1000.00. If the finance charge was $44.38, find the annual percentage rate of their loan.
15. A furniture store advertises recliner chairs for $299.95 with no down payment. Bob Charters decides to buy one of the chairs and signs a 90-day note in which he agrees to pay the full amount plus interest calculated at 18% per year. If, in addition to the interest, Bob is asked to pay a $10.00 service charge, what is the actual annual percentage rate of his loan?
16. Determine the finance charge and the annual percentage rate on an $800.00 loan for 90 days at an annual discounted interest rate of 15%.
In exercise 17 find the: a) the monthly payment, b) the total payment, and c) the finance charge.
17. An installment loan for $20,000.00 is to be repaid in equally monthly payments for 15 years with an annual percentage rate of 9%.
18. Sally Blackstone takes out a $1000.00 installment loan at an annual percentage rate of 14%. If Sally can afford to make payments of no more than $50.00 per month, which of the followings terms should Sally request?
- 6 months
- 12 months
- 18 months
- 24 months
- 30 months
19. For the loan in exercise 18, suppose that Sally could afford payments of up to $65.00 per month. Which term should she now choose and how much would she save in finance charges by choosing this shorter term?
In Exercises 20 to 29, consider a $500.00 installment loan to be repaid in six months with an annual percentage rate of 11.5%.
20. Find the monthly payment.
21. Find the interest payment for the first loan.
22. Find the balance after one payment.
23. Find the interest payment for the second month.
24. Continue the process started in exercise 21 to form an amortization schedule covering the entire term of 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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1
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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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25. Find the percentage of the total finance charge for this loan paid after the first payment.
26. Find the percentage of the total finance charge for this loan paid after the first two payments.
27. Suppose this loan were paid off at the time of the third monthly payment. What would the balance due be at this time?
28. Suppose this loan were paid off at the time of the fourth monthly payment. What would the balance due be at this time?
29. How much is saved in finance charges if the loan is paid off at the time of the third monthly payment?
30. Arlene Tompson borrows $2000.00 to purchase a piano. She has a choice of obtaining the loan from two different sources. One source offers her the loan for 24 monthly payments at an annual percentage rate of 14%. The second source offers the loan for 18 monthly payments at an annual percentage rate of 16%. Assuming she can afford the monthly payments for either plan, which should she choose in order to minimize her finance charges?