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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)
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: 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 (wtw» toe?” almywmaa 2. Consider an annuity making continuous payments with rate of payment function , 100(1 + 13/10)"l for 0 <15 < 10
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0 elsewhere. and accumulation function a(t) = (1 + 15/10) fort Z 0. Find the present value of this annuity. (12 pts)
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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)
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% 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:)
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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"? . leaasset 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)
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