Survey of Math Test #3 Practice Questions Page 1 of 5

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1 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 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 Consumer Prce Index: Not Seasonally Adjusted, U.S. cty average, All tems, Base Perod: =100. source: 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

2 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) $3100 D)$ (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) $ D) $ (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)

3 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 What would the cost of the house be n 2003 dollars? A) $14, B) $40, C) $1,6896,000 D) $38, (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) B) C) D) 36 Secton 3. Short Answer (1) The populaton of Chna n 2007 s 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 = 39 years. (10) If the populaton begns at 1.5, draw a cobweb dagram on the followng reproducton curve:

4 Test #3 Practce Questons Page 4 of 5 (2) The populaton of Chna n 2007 s 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( ) = 4.056(1.018) 33 = bllon (3) A populaton of 100 exhbts arthmetc growth of 10 unts per month. What s the populaton n after 1 year? = 220 (4) A car deprecates at 15% per year and cost $25,000 n What wll t s value be n 2010? $25, 000(1 0.15) 3 = $15, 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 ( /12) 360 $99, 000 = d ( /12) $99, 000 = d [160.29] d = $99, = $

5 Test #3 Practce Questons Page 5 of 5 The monthly payments are $ The nterest on the prncpal n the frst month s P = P r n = $99, = $ Therefore, $ 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 $ at the begnnng of the year and $ 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) $ = $ (1 + r) where we set k = 1 for one year r = $ $ = % Or you could get t from: r = $100 $ = %.