Test #3 Practce Questons Page 1 of 5 You wll be able to use a calculator, and wll have to use one to answer some questons. Informaton Provded on Test: Smple Interest: Compound Interest: Deprecaton: A = P (1 + rt) A = P (1 + ) n A = P (1 ) n Contnuous Interest: A = ( P e rt APY: = 1 + m) r m 1 Statc Reserve: = S U Geometrc seres: 1 + x + x 2 + + x n 1 = xn 1 [ x 1 (1 + ) n ] 1 Savngs formula: A = d [ ] Amortzaton formula: d = P 1 (1 + ) n Exponental Reserve: = ln [1 + (S/U)r] ln [1 + r] Year Annual Year Annual Year Annual Year Annual 1980 82.4 1986 109.6 1992 140.3 1998 163.0 1981 90.9 1987 113.6 1993 144.5 1999 166.6 1982 96.5 1988 118.3 1994 148.2 2000 172.2 1983 99.6 1989 124.0 1995 152.4 2001 177.1 1984 103.9 1990 130.7 1996 156.9 2002 179.9 1985 107.6 1991 136.2 1997 160.5 2003 184.0 Consumer Prce Index: Not Seasonally Adjusted, U.S. cty average, All tems, Base Perod: 1982-84=100. source: http://www.bls.gov/cp/home.htm Secton 1. True or False Crcle True (T) or False (F): (1) Compound nterest means you earn nterest on the prncpal only........................ T F (2) The amount of money after one year n an account that earns compound nterest ncreases as the tme perod for whch compoundng s appled ncreases................................. T F (3) Arthmetc growth s growth proportonal to the amount present......................... T F (4) Exponental decay s geometrc growth wth a negatve rate of growth.................... T F (5) Deprecaton of an tem s determned by usng a smple nterest formula................. T F (6) The Consumer Prce Index s needed to compare values of tems n dfferent years snce the rate of nflaton s not constant over tme...................................................... T F (7) When a loan s amortzed, the amount that s pad towards reducng the prncpal s the same each month.................................................................................. T F
Test #3 Practce Questons Page 2 of 5 Secton 2. Multple Choce Crcle the most approprate answer: (1) You have $2500 that you nvest at 6% smple nterest. What s the balance after four years? A) $310 B) $3000 C) $3100 D)$3156.19 (2) What s the Annual Percentage Yeld (APY) for an annual rate of 5.3% compounded quarterly? A) 5.3% B) 5.4% C) 5.5% D) 5.6% (3) You have $2500 that you nvest at 6% compound nterest, compounded monthly. What s the balance after four years? A) $3000 B) $3100 C) $3156.19 D) $3176.22 (4) What s the Annual Percentage Yeld (APY) for an annual rate of 6% compounded monthly? A) 0.500% B) 6.000% C) 6.090% D) 6.168% (5) The followng graph represents the amount of money n a savngs account, where there s an ntal amount deposted of $100 and no more deposts made. The nterest earned on the account s A) smple nterest. B) compound nterest compounded yearly. C) compound nterest compounded monthly. D) there s not enough nformaton gven to answer the queston. (6) Whch of the followng graphs could represent the accumulated balance on a bond whch earns compound nterest? A) B) C) D)
Test #3 Practce Questons Page 3 of 5 (7) If the annual nterest rate on a credt card s 6%, then the APR (annual percentage rate) s A) 6.00% B) 6.09% C) 6.18% D) 7.25% (8) A house cost $24,000 n 1987. What would the cost of the house be n 2003 dollars? A) $14,817.39 B) $40,787.24 C) $1,6896,000 D) $38,873.24 (9) The rule of 70 for populaton doublng says that a populaton that s growng at a constant rate of r% per year wll double n sze n A) 70 years B) 70/r years C) 70r years D) 70 r years (10) For the followng reproducton curve, the equlbrum populaton s A) 0 B) 1 C) 0.5 D) 2 E) There s no equlbrum F) Both A and B (11) For the logstc populaton model f(x) = 3x(1 x), f the startng populaton fracton s 0.4, then the next populaton fracton s A) 0.116 B) 0.416 C) 0.720 D) 36 Secton 3. Short Answer (1) The populaton of Chna n 2007 s 4.056 bllon people. The populaton s expected to grow at a rate of 1.8% per year. Use the rule of 70 to estmate how long t wll take for the populaton to double. 70 1.8 = 39 years. (10) If the populaton begns at 1.5, draw a cobweb dagram on the followng reproducton curve:
Test #3 Practce Questons Page 4 of 5 (2) The populaton of Chna n 2007 s 4.056 bllon people. The populaton s expected to grow at a rate of 1.8% per year. What wll the populaton be n 2040? 4.056(1 + 0.018) 2040 2007 = 4.056(1.018) 33 = 7.3076 bllon (3) A populaton of 100 exhbts arthmetc growth of 10 unts per month. What s the populaton n after 1 year? 100 + 10 12 = 220 (4) A car deprecates at 15% per year and cost $25,000 n 2007. What wll t s value be n 2010? $25, 000(1 0.15) 3 = $15, 353.10 Secton 4. Long Answer (1) You purchase a home for $99, 000 wth an annual nterest rate of 6.375% and a 30 year mortgage. What are your monthly payments, and how much of the frst monthly payment goes towards nterest? Frst, we need to know how much the monthly payment s for ths house. We can use the amortzaton formula to fgure ths out: [ ] 1 (1 + ) k P = d [ ] 1 (1 + 0.06375/12) 360 $99, 000 = d (0.06375/12) $99, 000 = d [160.29] d = $99, 000 160.29 = $617.631
Test #3 Practce Questons Page 5 of 5 The monthly payments are $617.63. The nterest on the prncpal n the frst month s P = P r n = $99, 000 0.06375 12 = $525.94 Therefore, $525.94 of the frst monthly payment goes towards nterest. The rest of the monthly payment reduces the prncpal. (2) Suppose that you have a bank account wth a balance of $4532.10 at the begnnng of the year and $4632.10 at the end of the year (you made no deposts to the account). What s the effectve nterest rate? The effectve rate s the rate we would have to use for smple nterest to get the amount over the same tme frame. The amount of nterest earned was $100.00, so the effectve rate r satsfes A = P (1 + kr) $4632.10 = $4532.10(1 + r) where we set k = 1 for one year r = $4632.10 $4532.10 1 = 2.2065% Or you could get t from: r = $100 $4532.10 = 2.2065%.