Date: Practice Test 6: Compound Interest

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Aubrey Townsend
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1 : Compoud Iterest K: C: A: T: PART A: Multiple Choice Questios Istructios: Circle the Eglish letter of the best aswer. Circle oe ad ONLY oe aswer. Kowledge/Thikig: 1. Which formula is ot related to compoud iterest? A (a) A P( 1 (b) P A( 1 (c) P ( 1 (d) P A (1 (e) A P( 1 2. Whe moey is ivested at 5% per year, compouded semi-aually, for five years, (a) 5 ad i (b) 5 ad i (c) 10 ad i (d) 10 ad i Whe chagig the compoudig period o a ivestmet, which statemet is true? (a) More frequet compoudig results i a greater amout of iterest. (b) More frequet compoudig results i the same amout of iterest. (c) More frequet compoudig results i a lesser amout of iterest. (d) More frequet compoudig chages both the pricipal ad amout, so there is o cosistet result. 4. Which of the followig sceario has ivestmet at the ed of the term? 8 A 5000(1.04) as the solutio to fid the amout of the (a) Nissa ivests $5000 at 4%, compouded aually for 8 years. (b) Toyota ivests $5000 at 8%, compouded semi-aually for 4 years. (c) Hoda ivests $5000 at 16%, compouded quarterly for 2 years. (d) All of the above (e) Noe of the above 5. For the formula I Prt, the uit for t must be i: (a) years (b) moths (c) weeks (d) days (e) hours 6. Ms. Chor ivested i a 180-day term deposit at the bak earig 4% simple iterest. She eared $ i iterest. How much did she receive at maturity? (a) (b) (c) (d) A $ debt is due i three years, ad iterest o the loa is 5% per year, compouded mothly. Calculate the discouted value of the loa today. (a) $ (b) $ (c) $ (d) $ (e) $ Page 1/ 6

2 Part B: True or False Questios Istructio: Read each of the followig statemets carefully. State whether each statemet is true (T) or false (F) i the space provided. Kowledge: 1. Simple iterest models liear growth; compoud iterest models quadratic growth. 2. Iterest is affected by the pricipal ivested, aual iterest rate ad legth of time ivested. 3. For A P( 1, is the umber of years moey has bee ivested or borrowed. 4. Loger term of ivestmet results i greater fial amout ad greater preset value. 5. Higher aual iterest rate results i lesser preset value ad greater fial amout. Part C: Full Solutio Questios Istructios: Show all steps for full mark. Marks will be deducted for poor or improper form. Provide aswer statemets i complete Eglish seteces where applicable. Kowledge: 1. How log does it take for a $2500 ivestmet to double its value at 5% simple iterest per year? [K: 3] 2. $3000 was ivested for 120 days ad made $35.51 i simple iterest. What was the aual iterest rate o the ivestmet? [K: 2] 3. A 9-moth GIC ears 4% simple iterest per year. What is the value of the GIC whe it matures if $5200 is ivested? [K: 3] Page 2/ 6

3 Commuicatio: 4. State the differeces betwee a ivestmet earig simple iterest ad a ivestmet earig compoud iterest. [C: 4] 5. Examie the give scree from the olie TVM Solver ad aswer the followig questios: (a) What is the compoudig frequecy if the term is 6 years? [C: 1] (b) What are the aual iterest rate ad the term if iterest is compouded quarterly? [C: 2] (d) Why is the future value egative? [C: 1] Page 3/ 6

4 6. Create a compoud iterest sceario with the fial amout calculated as A 2000(1 0.02). [C: 4] 6 7. Create a compoud iterest sceario with the pricipal calculated as P 4000(1 0.04). [C: 4] 12 Applicatio: 8. Eric eeds to borrow $2000. Which loa should he take? Justify your choice. [A: 8] Loa A: $2000 for three years at 10% per year, compouded semi-aually Loa B: $2000 for three years at 9.2% per year, compouded quarterly 9. Jeeva is 10 years old. His parets have decided to ivest some moey for his educatio, so that he will have $ at age 18 whe he goes to college. If the ivestmet ca ear 6.6% per year, compouded mothly, how much will his parets eed to ivest? [A: 4] Page 4/ 6

5 10. A $1000 ivestmet ears iterest at 4% per year, compouded quarterly. How log will it take to double the value of the ivestmet? [A: 4] Thikig: 11. Jay wats to buy a car. Which is the best deal, with iterest rates at 5% per year, compouded semi-aually? Justify your choice. [T: 8] Pla A: Pay $ i cash ow Pla B: Pay $1000 dow plus $ i oe year Pla C: Pay $500 dow plus $ i oe year 12. Emily borrowed $3600 at 6% per year, compouded quarterly. After the secod year, she repaid $2000. She is expected to repay the loa i full after four years. How much must she repay? [T: 4] Page 5/ 6

6 13. Elizabeth will iherit $ whe she turs 21 i six moths. She will borrow moey today to purchase a ew car ad will pay off the pricipal plus iterest i a lump sum with her iheritace. The bak offers short-term loas at a rate of 8% per year, compouded mothly. (a) How much ca Elizabeth borrow for the ew car? [T: 3] (b) How much of the $ paymet will be iterest? [T: 1] Aswers: Part A: Part B: 1. e; 2. c; 3. a; 4. d; 5. a; 6. c; 7. b 1. F; 2. T; 3. F; 4. F; 5. T Part C: years; %; 3. $5356; 4. Simple iterest grows liearly, but compoud iterest grows expoetially. Pricipal of simple iterest stays the same throughout the term, but pricipal of compoud iterest icreases by the average rate of iterest at the ed of each compoudig period, so there is a ew pricipal for each compoudig period throughout the term; 5. (a) semi-aually, (b) 6%, 3 years, (c) Either PV or FV must be egative for the program to work; 6. Aswer may vary. Nia ivests $2000 at 2% per year, compouded aually. What is the value of the ivestmet after 6 years? or JP ivests $2000 at 4% per year, compouded semi-aually. What is the value of the ivestmet i 3 years?; 7. Aswer may vary. Jemel eeds $4000 i 6 year. How much does he have to ivest today at 8% per year, compouded semi-aually? or Michael eeds $4000 i 1 year. How much does he have to ivest today at 48% per year, compouded mothly?; 8. Loa B, Repay $52.44 less for Loa B ( $ $ ); 9. $ ; years ad 6 moths; 11.Pla C, it has the least preset value or cost (A: $16250, B: $ , C: $ ); 12. $ ; 13. (a) $ , (b) $ Page 6/ 6

2. The Time Value of Money

2. The Time Value of Money 2. The Time Value of Moey Problem 4 Suppose you deposit $100 i the bak today ad it ears iterest at a rate of 10% compouded aually. How much will be i the accout 50 years from today? I this case, $100 ivested