DRAW TIME LINES! (Partial answers are given in brackets so show how to solve the problem and show complete final answers.)
1. During its 50-50 Sale, Marpole Furniture will sell its products for a 50% down payment (due date of sale), and the balance remaining to be paid in six months. No interest is charged for the first six months. If you wished to pay 100% on the due date instead, what amount would be equivalent to the 50/50 arrangement for a $1845 chesterfield* and chair set if Marpole can earn a rate of return of 10.75% on its funds? ($1797.94)
(*Canadian term for couch!)
2. Lydia purchased a $100,000 150-day T-bill when the prevailing yield on T-bills was 4.5%. She sold the T-bill 60 days later when the prevailing yield was 4.2%. What interest rate did Lydia earn during the 60-day period? (4.899%)
3. How much difference can 1% make? Compare the value of an investment of $10,000 after 25 years if it earns 6% compounded annually instead of 5% compounded annually? Calculate the difference in dollars and as a percentage of the smaller maturity value.
4. Nelson borrowed $5000 for 4 ½ years. For the first 2 ½ years, the interest rate on the loan was 8.4% compounded monthly. Then the rate became 7.5% compounded semiannually. What total amount was required to pay off the loan if no payments were made before the expiry of the 4 ½-year term? (7141.78)
5. A loan of $4000 at 7.5% compounded monthly requires three payments of $1000 at 6, 12, and 18 months after the date of the loan, and a final payment of the full balance after two years. What is the amount of the final payment? (1410.77)
6. What single payment one year from now would be equivalent to payments of $2500 due in three months, and another $2500 due in 2 years? Assume money can earn 7% pacq (compounded quarterly).
7. To motivate individuals to start saving at an early age, financial planners will sometimes present the results of the following type of calculation. How much must a 25-year-old individual invest five years from now to have the same maturity value at age 55 as an immediate investment of $1000? Assume that both investments earn 8% compounded annually. ($1469.33)
8. On the same date that the CIBC advertised rates of 2%, 2.5%, 3%, 3.25%, and 7% in successive years of its five-year compound-interest Escalating Rate Guaranteed Investment Certificate (GIC), it offered 2.75% compounded annually on its five-year fixed-rate GIC. How much more will a $10,000 investment be worth at the end of the five years if the Escalating Rate GIC is chosen instead of the fixed-rate GIC? (444.21)
9. How much money was needed 15 years ago to have the purchasing power of $1000 today if the (compound annual) rate of inflation has been:
10. An eight-year note for $3800 with interest at 11% compounded semiannually was sold after three years and three months to yield the buyer 14% compounded quarterly. What price did the buyer pay? (4655.39) (remember the two step!)
(KEY CONCEPT SECTION: DRAW TIME LINES!!)
11. Jorge is unable to make a $4500 payment due today. He proposes to settle the obligation by making three equal payments: one today, another in four months, and a third in nine months. What must each payment be to make the proposed payment stream equivalent to the scheduled payment if money can earn 7.2% compounded monthly? ($1539.02)
12. Payments of $400 due eight months ago and $650 due three months ago were not made. Now the debtor is proposing to "make good" by two future payments that provide for a 7.5% compounded monthly rate of return to the creditor on the missed payments. The first payment will be made in two months. The second payment, twice as large as the first, will be made in seven months. Determine the amount of each payment. (first is $373.06)
13. The owner of a residential building lot has received two purchase offers. Mrs. A is offering a $20,000 down payment plus $40,000 payable in one year. Mr. B's offer is $15,000 down plus two $25,000 payments due one and two years from now. Which offer has the greater economic value (that is, current day dollars) if money can earn 9.5% compounded quarterly? How much more is it worth in current dollars? ($2064.20)
Use a financial calculator for these questions. Make sure your final answer is complete. (Indicate interest rate basis (e.g. pacm) and time period.)
14. Mr. and Mrs. Markovich note that the home they purchased 20 years ago for $70,000 is now appraised at $340,000. What was the (equivalent) annual rate of appreciation in the value of their home during the 20-year period?
15. The maturity value of a $5000 four-year compound-interest GIC was $6147.82. What quarterly compounded rate of interest did it earn?
16. A four-year promissory note for $3800 plus interest at 9.5% compounded semiannually was sold 18 months before maturity for $4481. What quarterly compounded nominal rate of return will the buyer realize on her investment? (14%) (Note: Pay attention to compounding period in both steps.)
17. Your client invests $10,000 today at a rate of return of 7.7% compounded quarterly. Rounded to the nearest month, how long will it take the investment to grow to $22,000?
18. The proceeds from the sale of a $4500 five-year promissory note bearing interest at 9% compounded quarterly were $6055.62. How many months before its maturity date was the note sold if it was discounted to yield 10.5% compounded monthly? (17)
Use the equivalent rate formula for these questions. Make sure your answer indicate the compounding and time period.
19. Lisa is offered a loan from a bank at 7.2% compounded monthly. A credit union offers similar terms, but at a rate of 7.4% compounded semi-annually. Which loan should she accept? (Show calculations)
20. Columbia Trust wants its annually, semiannually, and monthly compounded five-year GICs all to have an effective rate of interest of 5.75%. What nominal annual rates should it quote for the three compounding options?
21. What monthly compounded interest rate is equivalent to:
- 6% compounded annually?
- 6% compounded semiannually? (5.93)
- 6% compounded quarterly?
22. You are offered a loan at a rate of 9% compounded monthly. Below what nominal rate of interest would you choose semiannual compounding instead? (9.17)