Question

Your friend offers to pay you an annuity of $6,300 at the end of each year for 3 years in return for cash today. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Select the correct answer.

a. $16,996.98

b. $17,002.88

c. $17,014.68

d. $17,020.58

e. $17,008.78

Answer 1

Solution:

The formula for calculating the present value of annuity assuming that it is an ordinary annuity:

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

Where

PV = Present value of annuity   ;   A = Amount of annuity   ;   r = rate of interest   ; n = no. of years

As per the information given in the question we have

r = 5.5 % = 0.055   ; n = 3 years   ; A = $ 6,300

Applying the above information in the formula we have

= $ 6,300 * [ ( 1 - ( 1 / ( 1 + 0.055 ) ³ )) / 0.055 ]

= $ 6,300 * [ ( 1 - ( 1 / ( 1.055 ) ³ )) / 0.055 ]

= $ 6,300 * [ ( 1 - ( 1 / 1.174241 )) / 0.055 ]

= $ 6,300 * [ ( 1 – 0.851614 ) / 0.055 ]

= $ 6,300 * [ 0.148386 / 0.055 ]

= $ 6,300 * 2.697933

= $ 16,996.980284

= $ 16,996.98   ( When rounded off to two decimal places )

The present value of the annuity = $ 16,996.98

Thus the amount that can be paid today = $ 16,996.98

Thus the solution is Option a. $ 16,996.98

Note: The value of ( 1.055 ) ³   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.055,3) = 1.174241