Question

For each of the following annuities, calculate the annual cash flow. (Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations. Round your answers to 2 decimal places (e.g.,32.16).) Cash Flow Future Value Interest Rate Years $ $ 25,450 4 % 8 $ 1,090,000 6 39 $ 928,000 7 25 $ 145,000 3 14

Answer 1

It is pressumed that the annual cash inflows are happening at the year end.

Cash Flow Future Value = Annual Cash flow X Fututre Value annuity factor,

Annual Cash flow = Cash Flow Future Value / Fututre Value annuity factor

Fututre Value annuity factor = (((1+i)ⁿ)-1) / (i) = ,

Here in case of first details

25,450

4%

8

i = 4%, n = 8 years or 8,

FV annuity factor = ((1.04⁸) - 1) / (0.04) = 9.21422626013185,

=25450 / 9.21422626013185 = 2762.03332558886,

Annual Cash flow (rounded to 2 decimal places) = $2762.03,

2nd  

10,90,000

6%

39years,

Cash Flow Future Value = Annual Cash flow X Fututre Value annuity factor,

Annual Cash flow = Cash Flow Future Value / Fututre Value annuity factor

Fututre Value annuity factor = (((1+i)ⁿ)-1) / (i) = , Here i = 6% or 0.06, n=39years or 39,

((1.06³⁹)-1) / (0.06) = 145.058458130911,

Annual Cash flow = 10,90,000 / 145.058458130911 = 7514.21195319963,

Annual Cash flow (rounded to 2 decimal places) = $7514.21,

for 3rd details,

9,28,000

7%

25 ,

Cash Flow Future Value = Annual Cash flow X Fututre Value annuity factor,

Annual Cash flow = Cash Flow Future Value / Fututre Value annuity factor

Fututre Value annuity factor = (((1+i)ⁿ)-1) / (i) = , Here i = 7% or 0.07, n=25years or 25,

Applyin values in formula, we will get ((1.07²⁵) - 1) / 0.07, = 63.2490377160413

Annual Cash flow = 928000 / 63.2490377160413,

=14672.1599807777

Annual Cash flow (rounded to 2 decimal places) = $14672.16,

for 4th details that is

1,45,000

3%

14years

Cash Flow Future Value = Annual Cash flow X Fututre Value annuity factor,

Annual Cash flow = Cash Flow Future Value / Fututre Value annuity factor

Fututre Value annuity factor = (((1+i)ⁿ)-1) / (i) = , Here i = 3% or 0.03, n=14years or 14,

Applyin values in formula, we will get ((1.03¹⁴) - 1) / 0.03, = 17.086324161837

Annual Cash flow = 145000 / 17.086324161837, = 8486.31915364588

Annual Cash flow (rounded to 2 decimal places) = $8486.32

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