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exam2-11sol

# exam2-11sol - STA 4183 Second Exam — Fall 2011 Name 1 An...

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Unformatted text preview: STA 4183 Second Exam — Fall 2011 Name: 1. An annuity makes annual payments at the beginning of each year for 20 years starting today. The ﬁrst five payments are for \$3,000 and the remaining payments are \$2,000. The annual effective interest rate is 5%. (a) Find the present value of this annuity. (14 pts) 0 ‘g‘ 5" LC? :9 M ‘EV! 7...; a®®® oqu. gown Qﬂﬁg m asiiﬂhetf +~ d2\$£{§,%§ : 3®y7if§n§ﬁl (b) This annuity was an inheritance that was purchased exactly 10 years ago (ie 10 years in the past from today). Assuming a consistent interest rate, what did it cost the person who bought the annuity? (4 pts) a go we 9 o m an (wt-w» toe?” almywmaa 2. Consider an annuity making continuous payments with rate of payment function , 100(1 + 13/10)"l for 0 <15 < 10 N) i 0 elsewhere. and accumulation function a(t) = (1 + 15/10) fort Z 0. Find the present value of this annuity. (12 pts) m if} 7L m 3% w, x i Mi “in ii 2.: y loo Cl he) (lye ‘ J0 N) (3 _ 1 __ E if) Z: - i o oo ( 1 + g. 0 gm (13) Find the accumulated value at t=1U. (4 pts) We“) 2:: WNW 3?» a9ng 3: WQQ 3. An annuity makes 12 total annual payments. Its ﬁrst payment is \$1,000 and is made exactly 5 years from today. Subsequent payments increase each year by 3% through the ﬁrst six payments. For the last 6 payments the annuity makes level pay- ments of \$2,000. Find the present value of this annuity. \ (18 pts) 0.9"}; genesis - at ; 'w‘ m.“ WW“? ‘ ‘ Q é l aliens. we page m J i l. 1 l l 5‘ F D ” wawmmamhwﬂwm‘w Essa a 5 i0 a? 2.0 e a PPVJ : "i" 09' ué- {O l- @6366 agile? : meet}? I“- <5§[email protected]§}y>é_ 5% «E— mmy {Sig-Law, % W \$3.: 55—— l... zoooﬂgmesmerj) + aeeoym<§.l§”75>mﬁs} 4. A loan with twenty equal annual payments is amortized using a 5% annual effective interest rate. The amount of interest on the 8th payment is \$444.44. Find the annual payment amount AND the total amount of the loan. ' (16 pts) lb: 016:) Inﬁaree’i: e 2%,. ? J” la- >< W. Wﬂfﬂﬁlmw : anneal: fag/Wﬁaf W teste‘zse ‘ l... 1-.» @‘aeeQCa-LW :t‘nmma f ar‘qa’mi {swan Smaémtrg 4 G" : 5. An annuity makes ﬁve \$501000 payments, one every four years with the ﬁrst pay- ment being made on January 1, 2013 and the last (ﬁfth) payment made on January 1, 2029. The annuity is based on an annual effective interest rate of 4%. Find the value of this annuity on January 1, 2012. '(16 pts) if a .r’ \$3; I w r: we -- new ’t Vﬁfmaea) ,2: 50000 a” ., ~ 6% '35"? . lea-asset 2 £33353 (307%???ié@> itaﬁiifig 4 6. An automobile installment loan of \$25,000 is repaid via payments made at the end of the each month for 5 years. The loan is structured according to the sinking fund method in which the loan has a nominal rate of 6% convertible monthly and the sinking fund earns interest at a 3% nominal rate convertible monthly. What are the monthly loan payments AND how much is deposited in the sinking fund each month? (16 pts) ) E g i; F :1” I @535“ Moa‘fﬂttxg interest . " - / “ ff"! a p' fl g 1:: g2?” m @5301? Mimi-3M7, ii beavsz Laval; Q5®©Q {bi} :5: L15 fie £53m ﬁ Meet) y I J ' 1' mm?“ in 3mm its .- 990;}; g 9:. L. Kaisee‘ﬁ? / new.th extra. neatly fem gay/ﬁren% ...
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