Question

You are searching the internet for investment opportunities and identify a 15-year annuity. The annuity will cost $42,000 today in exchange for 5.5 percent annual payments. What will the annual cash flow be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Multiple Choice $4,870.54 $4,466.82 $4,184.28 $4,811.74 $3,984.16

Answer 1

Solution:

The formula for calculating the present cost of annuity

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

where

PV = Present cost of annuity    ; ACF = Annual cash flow ;   r = rate of interest ; n = no. of years ;

As per the information given in the question we have

PV = $ 42,000 ; r = 5.5 % = 0.055   ; n = 15 years   ; ACF = To find ;

Applying the above information in the formula we have

$ 42,000 = ACF * [ ( 1 - ( 1 / ( 1 + 0.055 ) ¹⁵ )) / 0.055 ]

$ 42,000 = ACF * [ ( 1 - ( 1 / ( 1.055 ) ¹⁵ )) / 0.055 ]

$ 42,000 = ACF * [ ( 1 - ( 1 / 2.232476 )) / 0.055 ]

$ 42,000 = ACF * [ ( 1 – 0.447933 ) / 0.055 ]

$ 42,000 = ACF * [ 0.552067 / 0.055 ]

$ 42,000 = ACF * 10.037581

$ 42,000 / 10.037581 = ACF

ACF = $ 42,000 / 10.037581

ACF = $ 4,184.275099

ACF = $ 4,184.28 ( When rounded off to two decimal places )

Thus the Annual cash Flow = $ 4,184.28

The solution is option 3 = $ 4,184.28

Note: The value of ( 1.055 ) ¹⁵   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.055,15) = 2.232476