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Find the future values of these ordinary annuities. Compounding occurs once a year.
a.$400 per year for 10 years at 10%
b.$200 per year for 5 years at 5%
c.$400 per year for 5 years at 0%
d.Rework parts a, b, and c assuming they are annuities due.

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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

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