Question

What is the PV of an ordinary annuity with 10 payments of $67,450 if the appropriate interest rate is 71 percent?

7.1 percent

Answer 1

Solution:

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

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

Where

PV = Present value of annuity   ;   A = Annuity payment ;   r = rate of interest ; n = no. of payments ;

As per the information given in the question we have

r = 7.1 % = 0.071   ; n = 10    ; A = $ 67,450 ;

Applying the above information in the formula we have

= $ 67,450 * [ ( 1 - ( 1 / ( 1 + 0.071 ) ¹⁰ )) / 0.071 ]

= $ 67,450 * [ ( 1 - ( 1 / ( 1.071 ) ¹⁰ )) / 0.071 ]

= $ 67,450 * [ ( 1 - ( 1 / 1.985613 )) / 0.071 ]

= $ 67,450 * [ ( 1 – 0.503623 ) / 0.071 ]

= $ 67,450 * [ 0.496377 / 0.071 ]

= $ 67,450 * 6.991230

= $ 471,558.440878

= $ 471,558.4409    ( When rounded off to four decimal places )

= $ 471,558.44    ( When rounded off to two decimal places )

= $ 471,558   ( When rounded off the nearest dollar )

Thus the PV of an ordinary annuity with 10 payments of $ 67,450 if the appropriate interest rate is 7.1 percent = $ 471,558

Note: The value of ( 1.071 ) ¹⁰   is calculated using the Excel function =POWER(Number,Power)

=POWER(1.071,10) = 1.985613