Section I PROBLEMS Determine the number ofperiods and the rate per period for each ofthe following. RATE COMPOUNDED YEARS NO. OF PERIODS RATE PER PERIOD I. a. 7% Annually 6 b. 9 Quarterly 2 c. 10 Semiannually 4 d. 6 Monthly 3 e. II Semiannually 9 f 2. u. 5.H% Annually 8 b. 3 Monthly 4 c. 8 Semiannually 6 d. 8.5 Quarterly 4 c. 5.6 Semiannually 3 Find the compound amount and the compound interestfor each ofthe following. 3. $4,000 invested for 4 years at 7% compounded (a) annually and (b) semiannually. 4. $2,500 invested for 3 years at 5% compounded (a) annually and (b) semiannually. 5. $71,000 invested for 1 year at 5% compounded (a) semiannually and (b) quarterly. 6. $6,000 invested for 1 year at 8% compounded (a) semiannual1y and (b) quarterly. 7. $7,000 invested for 9 months at 6% compounded (a) quarterly and (b) monthly. 8. $4,500 invested for 6 months at 4.5% compounded (a) quarterly and (b) monthly. 9. Study carefully your answers to Parts (a) and (b) of the preceding problems. What conclusion seems to be indicated? 10. Suppose that you are given the principal, rate, and years of a compound interest problem. W'hat else must you know in order to work the problem? 496 Section 2 PROBLEMS 1-6. Rework Problems 3-8 of Section 1 (page 496) using the compound amount formula [M = P( 1 + i)tlJ. Compute the following compound amounts and compound interest, using Table 17. PRINCIPAL RATI! COMPOUNDED YEARS 7 a. $ 85,000 5% Monthly 3 b. 1.700 6 Quarterly 2 Co 45,000 7 Semiannually 6 d. 4,500 10 Monthly 4 e. 8,100 9 Annually 7 ; 8. a. $1,400 6% Monthly 5 b. 2,500 5 Quarterly 4 c. 5,200 4 Semiannually 3 d. 9,000 7 Monthly 6 e. 800 8 Quarterly 2 9. Compute compound amount and interest on the following deposits at 5% compounded monthly for 3 years. a. $500 b. $1,000 c. $2,000 d. What is your conclusion regarding the principal? 10. Compute compound amount and interest on the following investments at 7% compounded monthly for 4 years. a. $800 b. $1,600 c. $3,200 d. What is your conclusion regarding the principal? II. Calculate compound amount and interest on $ 1,000 drawing interest compounded quarterly for 2 years at the following rates. a. 4% b. 8% c. 16% d. Does doubling the rate exactly double the interest? 12. Determine compound amount and interest on $1,000 earning interest compounded quarterly for 5 years at the following rates. a. 3% b. 6% c. 12% d. Does doubling the rate exactly double the interest? 13. Determine compound amount and interest on $1,000 at 6% compounded semiannually for the following years. a. 2 years b. 4 years c. 8 years d. Does the interest exactly double when the time is doubled? 14. Compute compound amount and compound interest on $1,000 at 5% compounded semiannually for a. 3 years b. 6 years c. 12 years d. Does the interest exactly double when the time is doubled? 15. On January 1, 20X6, Marci Humble opened a savings account with a deposit of $1,000. Her bank paid 3% interest, compounded quarterly. a. What was the value of Humble's account on July I, 20X6? b. On that day, Humble made a deposit sufficient to bring the value of the account to $1,500. What amount did she deposit? c. How much was her account worth on July 1, 20X7? d. How much total interest did her account earn? 503 Section 3 PROBLEMS The following problems are all for interest paid at 4.5% compounded daily. Find (1) the amount ofinterest and (2) the balance at the end ofthe quarter for the following deposits. I. a. $9,300 on May 3 b. $800 on July 6 c. $4,000 on September 4 d. $600 on October 8 2. a. $1,000 on february 5 b. $350 on April 10 c. $2,300 on March 15 d. $700 on October J9 Compute the interest that would be earned for one quarter (1) at 4.5%, compounded daily, and (2) at 4.5%, compounded quarterly, on the given principals. The factor for 4.5%, compounded quarterly, for otle quarter is 0.01125. 3. a. 4 12,000 b. $4,500 4. a. $ 5,000 b. $ 600 Find (1) the total amount ofinterest and (2) the balance after the quarter ended for the following accounts. DEPOSII 5. a. $700 Oil October I $ 500 on October 22 $ 300 on November 15 $ 400 on December 5 b. $4,300011 Jalluary I 200011 Jalluary 30 $ 400 011 Februa ry 13 300 on A'larch 9 ,Ir 6. a. $1,000 on April 2 $ 200 on April 26 $ 500 on May 3 $ 400 on JUlle 28 b. $1 ,son 011 October I 900011 November I $1,000011 Novcmber 20 $ 600 on December 3 Compute (1) the interest for the quarter and (2) the balance when the quarter ended for the following problems. WITHDRAWAI.S 7. a. $10,000 all April I . 1,000 011 ~![ay 4 b. :;; 5,500 on lull' I ::; 100 all August 10 $ 400 on September l 8. a. $ 6,800 011 October 5 $ ROO 011 December 5 b. :;; 2,400 on January 10 $ 200 on February 8 $ 500 March 20 511 Section 4 PROBLEMS Compute present value at compound interest, using the data given in Problems 1 and 2. Also determine the amount ofinterest that will be earned before maturity. MATURITY VALUE RATE COMPOUNDED YEARS l. a. $14,600 4% Semiannually 2 b. 2,500 5 Quarterly 5 c. 6,800 7 Monthly 4 d. 9,500 5 Semiannually e. 4,400 6 Quarterly 3 # 2. a. $ 1,400 5% Quarterly 5 b. 40,000 8 Semiannually 3 c. 5,200 6 Monthly 6 d. 10,000 7 Quarterly 2 e. 8,700 5 Monthly 4 3. Bill and Beth Reno want to have $5,000 in savings in I year for a family vacation. If they can make an investment that pays 6%, compounded monthly, a. How much should the Renos invest now in order to have this maturity value? b. How much interest will their investment earn? 4. The Fannon Group wants to have $25,000 in savings in 2 years for a renovation project. a. What single deposit must be made now in a 2-year CD that earns 8% interest, compounded quarterly? b. How much interest will its investment earn? 5. The Capitol Plumbing Co. plans to increase the size of its warehouse in 2 years. The business will need $225,000 for the project. a. vVhat single deposit must be made now in an investment earning 8% interest, compounded quarterly? b. How much interest will the investment earn? 6. Furman Industries will require $30,000 in 2 years. If it can make an investment at 7%, compounded monthly, a. 'vVhat single deposit made now will yield this amount? b. How much interest will this investment earn? 7. Dominion Rentals, Inc., expects to remodel its offices in 6 years at a cost of $100,000. If the company can make an investment paying g°lt" compounded semiannually, a. What single deposit made now will produce this maturity value? b. How much interest will be included? 8. Dan's Boa~ ing Center expects to expand its operations in 5 years at a cost of $200,000. It can make an investment at 9%, compounded quarterly. a. \,."hat single deposit made now will produce this amount? b. How much interest will be earned? 9. An $85,000 investment is made at 6%, compounded quarterly, for a 4-year period. a. What ,is the maturity value of the investment? b. If money is generally worth 5%, compounded monthly, what is the present value of the investment?