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6. Calculating Annuity Values. For each of the following annuities, calculate the present value. Annuity Payment Years...

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Finance

6. Calculating Annuity Values. For each of the followingannuities, calculate the present value.

Annuity Payment Years Interest Rate

  $2,100    7 5%

1,095    9 10%

   11,000 18 8%   

30,000 28 14%

Answer & Explanation Solved by verified expert
3.8 Ratings (467 Votes)

a. Present value of annuities = Annuity * Present value of annuity of 1
= $             2,100 * 5.786373
= $     12,151.38
Working:
Present value of annuity of 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.05)^-7)/0.05 i           0.05
= 5.786373397 n 7
b. Present value of annuities = Annuity * Present value of annuity of 1
= $             1,095 * 5.759024
= $       6,306.13
Working:
Present value of annuity of 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.10)^-9)/0.10 i           0.10
= 5.759023816 n 9
c. Present value of annuities = Annuity * Present value of annuity of 1
= $           11,000 * 9.371887
= $ 1,03,090.76
Working:
Present value of annuity of 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.08)^-18)/0.08 i           0.08
= 9.371887136 n 18
d. Present value of annuities = Annuity * Present value of annuity of 1
= $           30,000 * 6.960662
= $ 2,08,819.87
Working:
Present value of annuity of 1 = (1-(1+i)^-n)/i Where,
= (1-(1+0.14)^-28)/0.14 i           0.14
= 6.96066228 n 28

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