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Submitted By krasinski
Words 314
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Problem 1

The formula is FV (C , r , T ) = C ∗ (1 + r )T = 1000 ∗ (1.05)T (1)

which gives 1276.28, 1628.89 and 2078.93 for T = 5, 10, 15 respectively.

Patrick C Kiefer

408 Lukas PS1

Problem 2

Now the formula is PV (C , r , T ) = 500 C = T (1 + r ) (1.04)T (2)

which equals 480.77, 462.28, 410.96 for T = 1, 2, 5 respectively.

Patrick C Kiefer

408 Lukas PS1

Problem 3

The EAR is given by r 1 EAR(r , n) = (1 + )n − 1 = (1 + )12 − 1 = .010045 > .01 n 12 You can see that the eﬀective rate is slightly more than the quoted rate.

Patrick C Kiefer

408 Lukas PS1

Problem 4
Now we use
T

PV (C , r , T ) = i=1 C = 100 (1 + r )i

5

i=1

1 = 421.24 (3) (1.06)i

Notice that for computational convenience, the shortcut annuity formula is more tractable: PV (C , r , t) = C ∗ 1 r 1− 1 (1 + r )T (4)

Patrick C Kiefer

408 Lukas PS1

Problem 5
We use
T

NPV (I , C , r , T ) = −I + i=1 C 500 = −10, 000+ T (1 + r ) (1.04)i i=1

The perpetuity formula is

i=1

C C = i (1 + r ) r

(5)

so the NPV is -10,000+12,500 = 2,500 for r = .04. For r = .05, the NPV is zero. Note the solution for r = .05 and g = .01 coincides with the solution for r = .04.
Patrick C Kiefer 408 Lukas PS1

Problem 6

We use a combination of the formulas introduced above
T

−12, 000 + i=1 1, 000 1 400 + = 671.10 > 0 (1.04)i (1.04)5 .04

(6)

So, take the project if you do not have to turn down another one with a higher NPV.

Patrick C Kiefer

408 Lukas PS1