Engineering Economic Analysis for Sustainable Energy

Assignment due on 09/15/2015

Question 3-11

P = $5000000

n= 5 years

i= 10%

For lumpsome,

F= P[F/P, I , n]

F= 5000000[1.611]

F= $8,055,000

Question 3-22

i=8%

P= $1000

F= P(1+i)n

n= ln(F/P)/ln(1+i)

a) F= 1360

n= ln(1.360)/ln(1+0.08)

n= 3.9953 years == 4 years

b) F= 2720

n= ln(2.72)/ln(1.08)

n= 13.001 years

c) F= 4316

n= ln(4.316)/ln(1.08)

n= 19.0011 years

d) F= 6848

n= ln6.848 / ln1.08

n= 24.99909 == 25 years

Question 3-45

P= 75

F= 85

85= 75(1+i)1

1+i = 85/75 = 1.1333

i= 0.1333

Nominal Interest rate = 0.1333 (2) (100) = 26.66%

Effective interest rate = (1+0.2666/2)2 – 1

Effective Interest rate, ia , = 28.43 %

Question 4-4

F= 35.96

A= 1

F= A{ [(1+i)n -1]/i}

3.595 = 1.1n -1

ln 4.595 = n ln 1.1

n= 16.00 years

Question 4-15

P = $16500

Sales Tax = 0.08 * 16500

= 1320

a) Total cash paid when car id purchased = 10% of car value+ Sales Tax+450

= 1650 + 1320 + 450

= $3420

b) P = remaining value of car not paid = 14850

r = 9%

i= 9/12 = 0.75 %

m = 48

F= 14850(1+0.75)48

F= 21256.3692

Monthly Payment = A = F{i/[(1+i)n -1] }

A= F [ 0.0075 /{ (1.0075)48 – 1 } ]

A = $369.5474

Question 4-33

Using the formula for present value we get

PV = 0 = 300/1.1 + 200/1.12 + 100/1.13 + 200/1.14 + 100-E/1.15 + 200-E/1.16 + 300/1.17

272.2+165.25+75.13+136.60+153.94 + 100-E/1.15 + 200-E/1.16 = 0

803.12 *1.15 + 100 – E + 200-E/1.1 = 0

1393.43 – E + 200-E/1.1 = 0

1532.77 + 200 = 2.1 E

E = 825.13

Question 4-58

Using the formula for present value we get:

PV = 0 = 100/1.12 + 200/1.13 + 300/1.14 + (-C)/1.16 + (-C)/1.17 + (-C)/1.18

(1.21 +1.1+1) C = 82.64 + 150.26 + 204.90

C= 938.46/3.31

C = 283.523

Question 4-84

P= $20000

a) P = 20000[P/A, 10, 10] + 2000[P/G, 10 , 10]

P = 20000* 6.145 + 2000*22.891

P = 122900+45782

P= 168682

b) We use the formula P = A1[n(1+i)-1 ], because g= i = 10% .

P = 20000[10/(1+0.1)]

P = 181818.18

Question 4-118

We do not need to calculate each amount sepeately. As Barry is depositing the same amount of

money each quarter to each bank, the bank with higher effective interest rate will provide more

interest.

Calculating Effective Annual Interest rate, ia .

Bank 1: ia = er – 1

ia = e0.045 – 1

ia = 1.046027-1

ia = 4.603 %

Bank 2:

ia = (1+ 0.046/12) 12 – 1

ia = 1.04698 – 1

ia = 4.698%

As the ia for Bank 1 < bank 2 , Barry made the wrong decision.

Question 3- 56

P = $10000

r= 6.50 %

When compounded daily

m = 365

F = 10000(1+0.065/365)365

F = 10671.5284

When compounded continuously

F = Pern

n= 1 ; r= 6.50%

F= 10000 * e0.065

F = $10671.59024

Therefore after depositing with South Bank, we get an increased interest of 6.1 cents.