Question

If you put up $32,000 today in exchange for a 8.6 percent, 11-year annuity, what will the annual cash flow be? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Answer 1

Solution:

The formula for calculating the annual cash flow for an annuity of “n” years where the PV of the series of annual cash Flows is given is

PV = ACF * [ ( 1 - ( 1 / ( 1 + r ) ⁿ )) / r ]

PV = Present value of series of annual cash Flows

ACF = Annual cash flow or Annuity payment

r = rate of interest ; n = no. of years

As per the information given in the question we have

PV = $ 32,000 ; r = 8.6 % = 0.086   ; n = 11 years   ; ACF to find

Applying the above information in the formula we have

$ 32,000 = ACF * [ ( 1 - ( 1 / ( 1 + 0.086 ) ¹¹ )) / 0.086 ]

$ 32,000 = ACF * [ ( 1 - ( 1 / ( 1.086 ) ¹¹ )) / 0.086 ]

$ 32,000 = ACF * [ ( 1 - ( 1 / 2.478153 )) / 0.086 ]

$ 32,000 = ACF * [ ( 1 – 0.403526 ) / 0.086 ]

$ 32,000 = ACF * [ 0.596474 / 0.086 ]

$ 32,000 = ACF * 6.935740

$ 32,000 / 6.935740 = ACF

ACF = $ 32,000 / 6.935740

ACF = $ 4,613.7832

ACF = $ 4,613.78 ( When rounded off to two decimal places )

If we put up $32,000 today in exchange for a 8.6 percent, 11-year annuity, the annual cash flow be = $ 4,613.78

Note: The value of ( 1.086 ) ¹¹   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.086,11) = 2.478153