Question

What is the present value of

$2,000

paid at the end of each of the next

84

years if the interest rate is

8%

per​ year?

Round to the nearest cent

Answer 1

Solution:

The formula for calculating the present value of annuity is :

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 = 8 % = 0.08   ; n = 84 years   ; A = $ 2,000 ;

Applying the above information in the formula we have

= $ 2,000 * [ ( 1 - ( 1 / ( 1 + 0.08 ) 84 )) / 0.08 ]

= $ 2,000 * [ ( 1 - ( 1 / ( 1.08 ) 84 )) / 0.08 ]

= $ 2,000 * [ ( 1 - ( 1 / 642.089342 )) / 0.08 ]

= $ 2,000 * [ ( 1 – 0.001557 ) / 0.08 ]

= $ 2,000 * [ 0.998443 / 0.08 ]

= $ 2,000 * 12.480532

= $ 24,961.064608

= $ 24,961.06    ( When rounded off to the nearest cent )

The present value of $ 2,000 paid at the end of each of the next 84 years if the interest rate is 8% per​ year = $ 24,961.06

Note: The value of ( 1.08 ) 84   is calculated using the Excel function =POWER(Number,Power)

=POWER(1.08,84) = 642.089342