Math 1030Q Spring Exam #2 Review. (9.2) 8x = log (9.2) 8x = log.32 8x log 9.2 log log log 9.2. x =.06418
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1 Math 1030Q Sprig 2013 Exam #2 Review 1. Solve for x: x = 2.32 Solutio: x = x = log 9.2 8x = log.32 8x log 9.2 = log.32 8x log 9.2 log.32 = 8 log log 9.2 x = Solve for y: 3y 7 13 = 1540 Solutio: 3y 7 13 = 1540 y 7 13 = y 7 = y =
2 3. Which will be worth more i 10 years: $10,000 ivested at 8.2% simple iterest, or $10,000 ivested at 5% iterest, compouded mothly? Solutio: For simple iterest: F = = $18,200 For compoud iterest: F = = = = $16, so you ear more with simple iterest. 4. Suppose a fried leds you $100, ad you agree to pay him back $1 i 18 moths. If we assume that this is simple iterest, the what is the iterest rate? Solutio: Note that 18 moths is t = 1.5 years. The solvig for r, F = P rt 1 = r 1. = 1.5r 0. = 1.5r 0.08 = r = 8%
3 5. For a accout with a aual iterest rate of 6%, fid the aual percetage yield APY if iterest is compouded: a quarterly? Solutio: APY = = = = 6.14% b mothly? Solutio: APY =.06 1 = = = 6.17% c daily? Solutio: APY =.06 1 = = = 6.18%
4 6. A bak advertises a Certificate of Deposit CD with 4.8% iterest, compouded mothly. If I ivest $3,500 today, how log will it take for my ivestmet to grow to $4,200? Solutio: Usig the compoud iterest formula ad solvig for t, F = P r t 4200 = t 1.2 = t log1.2 = log t log1.2 = t log log1.2 = t log1.004 log1.2 = t = years log Reba would like to make the $2,150 dow paymet o a ew car i 6 moths. If she has $2,000 i her savigs accout, ad iterest is compouded daily, what iterest rate would she eed to ear to have eough? Solutio: Usig the compoud iterest formula t must be i years, ot moths: 2150 = 2000 r 2150 = 2000 r = r = r = r = r = r = r 14.47%
5 8. Whe Jed was bor, his gradfather deposited $1,982 ito a savigs accout for his gradso, uder the coditio that obody touches it util Jed turs 21. If this accout ears 3.9% iterest compouded semi-aually twice per year, the how much will Jed have o his 21st birthday? Solutio: Usig the compoud iterest formula ad solvig for F, F = P r t = = = = $4, May years later, Jed s graddaughter is bor, ad he would like to do somethig similar for her. He would like her to have exactly $10,000 i the accout o her 21st birthday. If the accout ears 4.1% compouded aually, how much would Jed eed to deposit o the day she is bor? Solutio: = P = P = P = P P = $4,300.66
6 10. It s ever too early to start savig for retiremet! Suppose you fid a savigs accout that will pay 5% iterest compouded mothly. If, startig o your ext birthday, you deposit $85 per moth, ad cotiue this util your 65th birthday, how much will you have i your accout? Solutio: This depeds o your curret age, obviously, so let s assume you do this startig whe you tur 21. The o your 65th birthday you ve bee makig deposits for t = = 44 years. Usig the systematic savigs formula ad solvig for F, r t F = D 1 r = = = = = $162, Let s say you d like to retire with, oh I do t kow, $1 millio. Give the same accout from #10, how much would you eed to deposit every moth for this to happe? Solutio: Assume you start o your 21st birthday = D = D = D = D = D D = $521.89
7 . Maggie borrows $7,000 from the bak at 8% iterest compouded mothly. a If she makes a $400 paymet at the ed of the first moth, how much does she owe? Solutio: This is the remaiig balace etry that would be at the ed of the first row of a amortizatio schedule. It would read Paymet Iterest Paid Pricipal Paid Remaiig Balace 0.08 $ = = = $6, b If she cotiues payig $400 mothly, how log will it take to pay off the loa? Solutio: Usig the loa formula ad solvig for t, 1 r P = R 7000 = 400 r t = t = t = t log = log t log = t log log = t = years log t
8 13. Adrew takes out a $18,500 studet loa to pay for graduate school. If the iterest rate is 6.3% compouded quarterly, how large would his quarterly paymets be i order to pay off this loa i 10 years? Solutio: Usig the loa formula ad solvig for R, 1 r t P = R = R r = R = R R = = $ Fray ad Zooey are ready to buy their first house. They determie that they ca pay $1100 per moth towards a mortgage. If the 20 year mortgage available to them charges 7.8% iterest compouded mothly, a how large of a loa ca they afford? Solutio: Usig the loa formula ad solvig for P, 1 r t P = R = 1100 r = = = 1100 = $133,
9 b create a amortizatio schedule for the first 3 moths of the loa. Solutio: The rows detailig the first three mothly paymets would read Paymet Iterest Paid Pricipal Paid Remaiig Bal. $133, = $ = $ $133, = $ = $ $133, = $ = $ $132, Whe rollig two dice, what is the probability that you: a Roll a 5? Solutio: You could have 1,4, 2,3, 3,2, 4,1 as possible rolls. There are 36 total possibilities, so P 5 = 4 36 = 1 9. b Roll a umber higher tha 9? Solutio: You could have 4,6, 5,5, 6,4, 5,6, 6,5, 6,6 as possible roll, so P 9 = 6 36 = 1 6. c Do t roll a 3? Solutio: We kow we could have 1,2 or 2,1 as our possible outcomes for rollig a 3, so to fid P ot 3, we have P ot 3 = 1 P 3 = 1 2 = 34 = d Roll a umber that is at least 5? Solutio: We could cosider all outcomes that result i 5 or higher, but there are a lot of those, so it will be faster to otice that the oly outcomes which are ot 5 or higher are the oes which are less tha 5, i.e. 1,1, 1,2, 1,3, 2,1, 2,2, ad 3,1. So P 5 = 1 P 4 = 1 6 = 30 = e Roll a eve umber or a umber larger tha 3? Solutio: Use the additio rule. Clearly half of the possible outcomes are eve ad half are odd, so P eve = P > 3 =, sice every outcome except for 1,1, 2,1, ad 1,2 is larger tha 3. Of the 18 eve outcomes, oly 1,1 is ot larger tha 3, so P eve AND > 3 = 17, ad thus our fial aswer is 36 P eve OR > 3 = = 34 =
10 16. Accordig to the America Medical Associatio, i 1996 there were 737,764 physicias i the Uited Sates, 157,387 of whom were female. There were 133,005 physicias uder 35 years of age, 47,348 of whom were female. What is the probability that a radomly chose physicia i 1996 was female or uder the age of 35? Solutio: P female OR 35 = P female + P 35 P female AND 35 = = = = 32.9% 17. A recet poll at a uiversity shows that, i a vote for the ew mascot: 60% of studets would approve of a giraffe, 42% would approve of a hippo, ad 17% would approve of both. If we select a studet at radom, what s the probability that he or she would approve of either the giraffe or the hippo? Solutio: Notice that P either A or B = 1 P either A or B... The P G or H = P G + P H P G ad H = = 0.85, so, P either G or H = = 0.15 = 15%.
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