ECOR 3800 Study Guide - Quiz Guide: Cadillac, Cadillac De Ville Series, Engineering Economics
21 Apr 2019
School
Department
Course
Professor
1
Carleton University
Department of Civil and Environmental Engineering
Engineering Economics (ECOR 3800)
ASSIGNMENT # 2-solution
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Question (1) (20 marks)
(A)
The Cadillac Motor Car Company is advertising a 20 month lease of a Cadillac DeVille for $720,
payable at the beginning of each month. The lease requires a $3500 down payment, plus a $500
refundable security deposit. As an alternative, the company offers a 24-month lease with a single
up-front payment of $15660, plus a $600 refundable security deposit. The security deposit will be
refunded at the end of the 20-month lease. Assuming an interest rate of 6.3%, compounded
monthly, which lease is proffered one?
Solution
r = 6.3%, M = 12, i
month
= 0.525
• 20-month lease plan:
P = ($3500 + $720 + $500) + $720(P/A, 0.525%, 19) - $500(P/F, 0.525%, 20)
=$17257
• Up-front lease plan:
P = $15660 +$600 - $600(P/F, 0.525%, 20) = $15719
∴ Select up-front lease plan
2
B)
How many years will it take an investment to triple if the interest rate is 3% compounded
(a) Quarterly? (b) Monthly? (c) Continuously?
Solution
(a) Quarterly interest rate = 0.75%
3P = P (1 + 0.0075)
N
log 3 = N log 1.0075
N = 147 quarters
∴ 147 / 4 = 36.76 years
(b) Monthly interest rate = 0.25%
3P = P (1 + 0.0025)
N
log 3 = N log 1.0025
N = 439.99 months
∴ 439.99 / 12 = 36.67 years
(c)
3 = e
0.03N
ln(3) = 0.03 N
N = 36.62 years
3
(C)
You have a habit of drinking a cup of Starbucks coffee ($1.8 a cup) on the way to work every
morning. If, instead, you put the money in the bank for 25 years, how much would you have at the
end of that time, assuming that your account earns 6% interest compounded daily? Assume also
that you drink a cup of coffee every day, including weekends.
i = e
0.06/365
- 1 = 0.0164397%
F = $1.8(F/A, 0.0164397%, 9125) = $38119.84
Question (2) (20 marks)
(A) Consider the following cash flows and compute the equivalent annual worth at
i = 7%,
A
n
n Investment Revenue
0 -10,000
1 3000
2 3000
3 4000
4 4000
5 2000
6 +2000 200
Solution
AE(7%)=
[-10,000+3,000* (P/A,7%,2)+ 4,000* (P/A,7%,2)*(P/F,7%,2)+2000*(P/F,7%,5)
+(2,000+200)*(P/F,7%,6)] *(A/P,7%,6)
= [-10,000+3,000* (1.808)+ 4,000* (1.808)*(0.8734)+2000*(0.713)
+(2,000+200)*(0.6663)] *(0.2098)
= $971.85
Document Summary
The cadillac motor car company is advertising a 20 month lease of a cadillac deville for , payable at the beginning of each month. The lease requires a down payment, plus a refundable security deposit. As an alternative, the company offers a 24-month lease with a single up-front payment of , plus a refundable security deposit. The security deposit will be refunded at the end of the 20-month lease. Solution r = 6. 3%, m = 12, imonth = 0. 525: 20-month lease plan: P = ( + + ) + (p/a, 0. 525%, 19) - (p/f, 0. 525%, 20) P = + - (p/f, 0. 525%, 20) = . 3p = p (1 + 0. 0075)n log 3 = n log 1. 0075. 147 / 4 = 36. 76 years (b) monthly interest rate = 0. 25% 3p = p (1 + 0. 0025)n log 3 = n log 1. 0025. 439. 99 / 12 = 36. 67 years (c)
