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Unformatted text preview: (a ME 3232 — Homework #1; Due September 22, 2010 . How much invested now at 6% would be just suﬂicient to provide three payments with the ﬁrst payment in the amount of $2000 occurring 2 years hence, $3000 ﬁve years hence, and
$4000 seven years hence? . What is the present worth of the following series of payments? a. $1200 at the end of eﬂar for 12 years at 6%, compounded annually
b. $2000 at the end of each year for 10 years at 9%, compounded annually
c. $500 at the end of each year for 5 years at 7.25%, compounded annually d. $4000 at the end of the year for 8 years at 8.75%, compounded annually . At what rate of interest, compounded annually, will an investment double itself in 10 years? . What is the equal payment series for 10 years that is equivalent to a payment series of $12,000 at the end of the ﬁrst year, decreasing by $1000 each year over the next 9 years.
Interest is 8%, compounded annually. . On the day his baby was born, a father decided to establish a savings account for his child’s
‘ "university'édiication. Any money that is put iritb the account will earn an interest rate of 8%, compounded annually. He will make a series of annual deposits in equal amounts on each of
his child’s birthdays from the ﬁrst through the child’s 18 , so that his child can make four
annual withdrawals from the account in the amount of $20,000 on each of his birthdays.
Assuming that the ﬁrst withdrawal will be made on the child’s 18‘ll birthday, which of the
following statements are correct to calculate the required annual deposit? a. A = ($20,000 x 4)/ 18
‘9 b. A = $20,000(F/A,8%,4)(P/F,8%,21)(A/P,8%,18) c. A = $20,000(P/A,8%,18')(F/P,8%,21)(A/F,8%,4)
a d. A = [ $20,000(P/A,8%,3) + $20,000 ](A/F,8%,18)
ge. A = $20,000[(P/F,8%,18) + (P/F,8%,l9) + (P/F,8%,20) + (P/F,8%,21)](A/P,8%,18) . The Sporting News carried the following story on June 19, 1989: Dallas Cowboys quarterback Troy Aikman, the number one pick in the National Football
League raft, will earn either $11,406,000 over 12 years or $8,600,000 over 6 years. Aikman,
represented by Leigh Steinberg, must declare which plan he prefers. The $11 million package
is deferred through the year 2000, while the nondeferred arrangement ends aﬁer the 1994
season. Regardless of which plan is chosen Aikrnan will be playing through the 1994 season.
a. As it happens, Troy was under the nondeferred plan prior to his much publicized $50
million contract in 1993. In retrospect, if Aikman’s interest rate were 6%, did he
make a wise decision in 1989?
b. At what interest rate would the two plans be economically equivalent?
Note that a table of annual compensation rates for Aikman’s contract options follows. _. \. _.~_,.V..,<:‘_:,3_ooo.(_E_/‘ 3, l“ the 31—51 L; I S c9 0 ‘L
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I‘. _.H______;1L1,33\, 57.0 ME 3232 — Homework #2; Due September 29, 2010 War Eagle Financial Sources, which makes small loans to college students, offers to lend
$400. The borrower is required to pay $26.61 at the end of each week for 16 weeks.
Find the interest rate per week. What is the nominal interest rate per year? What is the
effective interest rate per year? The Cadillac Motor Car company is advertising a 24month lease of a Cadillac Deville
for $470 payable at the end of each month. The lease requires a $2200 down payment,
plus a $500 refundable security deposit. As an alternative, the company offers a 24
month lease with a single upfront payment of $11,970, plus a $500 reﬁmdable security
deposit. The security deposit will be reﬁmded at the end of the 24month lease.
Assuming an interest rate of 6%, compounded monthly, which lease is the preferred one? What is the future equivalent of a series of equal monthly payments of $2000, if the
series extends over a‘period of 6 years at 12% interest, compounded as follows: (a) Quarterly,
(b) Monthly,
(0) Continuously? Emily Lacy received $250,000 ﬁom an insurance company after her husband’s death.
Emily wants to deposit this amount in a savings account which earns interest at a rate of
6%, compounded monthly. Then, she would like to make 60 equal monthly withdrawals
over the 5year deposit period, such that, when she makes the last withdrawal, the savings
accounts will have a balance of zero. How much can she withdraw each month? Consider the cash ﬂow diagram, which represents three different interest rates applicable
over the 5 year time span. (a) Calculate the equivalent amount P at the present.
(b) Calculate the single—payment equivalent to F at n = 5.
(0) Calculate the equalpaymentseries case ﬂow A that runs from n = 1 to n = 5. $3000 $ 2000 $2000 $2000 $2000 O : :2 I4 5 (3% E 10% 58% Ye“
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P quarterly : quarterly I quarlerly Talhi Haﬁd is considering the purchase of a used automobile. The price including the
title and taxes is $8260. Talhi is able to make a $2260 down payment. The balance,
$6000, will be borrowed from his bank at an interest rate of 9.25%, compounded daily. The loan should be paid in 48 equal monthly payments. Compute the monthly payment.
What is the total amount of interest he has to pay over the life of the loan? You are buying a home for $175,000. If you make a down payment of $3 0,000 and take
out a mortgage on the rest at 8.5%, compounded semiannually, what will be your monthly payment to retire the mortgage in 15 years? A $1000, 9.50% semiannual bond is purchased for $1010. If the bond is sold at the end
of 3 years and six interest payments, what should the selling price be to yield a 10%
compounded semiannually return on your investment? You are considering buying a new car worth $15,000. You can ﬁnance the car by either
withdrawing cash ﬁom your savings account, which earns 8% nominal interest (you
determine the compounding period based on the following information), or by borrowing
$15,000 ﬁ‘om your dealer for 4 years at 11% nominal (you determine the compounding
period). You could earn $5635 in interest from your savings account for 4 years if you
left the money in the account. If you borrow $15,000 from your dealer, you only pay
$3609 in interest over 4 years, so it makes sense to borrow for your new car and keep
your case in your savings account. Do you agree or disagree with the statement above?
Justify your reasoning with a numerical calculation. 35 'ILQ‘VG'I
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