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
