Answer:
a. $6,374.97
b. $1,105.13
c .$400
d. (a) $7,012.47, (b) $1,160.38 (c) $400
Explanation:
P = C [((1+r)^n)-1)/r]
Where:
P = Future value of the annuity stream to be paid in the future
C = Value of each annuity payment
r = Interest rate
n = Number of periods over which payments are made
a. P = C [((1+r)^n)-1)/r]
C = $400
r = 10%
n = 10
P = 400 [((1 + 10%)^10) - 1) / 10%]
P = 400 [((1.1)^10) - 1) / 0.1]
P = 400 [(2.593742460 - 1) / 0.1]
P = 400 [(1.593742460) / 0.1]
P = 400 [(15.93742460]
P = 6,374.969840
P = $6,374.97
b. P = C [((1+r)^n)-1)/r]
C = $200
r = 5%
n = 5
P = 200 [((1 + 5%)^5) - 1) / 5%]
P = 200 [((1.05)^5) - 1) / 0.05]
P = 200 [(1.276281563 - 1) / 0.05]
P = 200 [(0.276281563) / 0.05]
P = 200 [(5.525631250]
P = 1,105.126250
P = $1,105.13
c. P = C [((1+r)^n)-1)/r]
C = $400
r = 0%
n = 5
P = 400 [((1 + 0%)^5) - 1) / 0%]
P = 400 [((1)^5) - 1) / 0]
P = 400 [(1 - 1) / 0]
P = 400 [(0) / 0]
P = 400 [Undefined]
P = 400
P = $400
d. (a) FV of Annuity Due = P = C [((1+r)^n)-1)/r] x (1+r)
C = $400
r = 10%
n = 10
P = C [((1+r)^n)-1)/r]
C = $400
r = 10%
n = 10
P = 400 [((1 + 10%)^10) - 1) / 10%] x (1+10%)
P = 400 [((1.1)^10) - 1) / 0.1] x (1+0.1)
P = 400 [(2.593742460 - 1) / 0.1] x (1.1)
P = 400 [(1.593742460) / 0.1] x (1.1)
P = 400 [(15.93742460] x (1.1)
P = 6,374.969840 x (1.1)
P = 7,012.466824
P = $7,012.47
d. (b). P = C [((1+r)^n)-1)/r] x (1+r)
C = $200
r = 5%
n = 5
P = 200 [((1 + 5%)^5) - 1) / 5%] x (1+5%)
P = 200 [((1.05)^5) - 1) / 0.05] x (1.05)
P = 200 [(1.276281563 - 1) / 0.05] x (1.05)
P = 200 [(0.276281563) / 0.05] x (1.05)
P = 200 [(5.525631250] x (1.05)
P = 1,105.126250 x (1.05)
P = $1,160.382563
P = $1,160.38
c. P = C [((1+r)^n)-1)/r] x (1+r)
C = $400
r = 0%
n = 5
P = 400 [((1 + 0%)^5) - 1) / 0%] x (1+0%)
P = 400 [((1)^5) - 1) / 0] x (1.0)
P = 400 [(1 - 1) / 0] x (1.0)
P = 400 [(0) / 0] x (1.0)
P = 400 [Undefined] x (1.0)
P = 400 x (1.0)
P = $400
