Question

If the current rate of interst is 8%, what is the Present Value of an investment that pays $1000 per year and lasts 20 years?

Answer 1

Solution :

The formula for calculating the present value of an investment that pays an annuity or annual payments :

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

Where

PV = Present value of investment ;   A = Amount of annuity or annual receipt   ;   r = rate of interest ;

n = no. of years

As per the information given in the question we have

r = 8 % = 0.08   ; n = 20 years   ; A = $ 1,000

Applying the above information in the formula we have

= $ 1,000 * [ ( 1 - ( 1 / ( 1 + 0.08 ) ²⁰ )) / 0.08 ]

= $ 1,000 * [ ( 1 - ( 1 / ( 1.08 ) ²⁰ )) / 0.08 ]

= $ 1,000 * [ ( 1 - ( 1 / 4.660957 )) / 0.08 ]

= $ 1,000 * [ ( 1 – 0.214548 ) / 0.08 ]

= $ 1,000 * [ 0.785452 / 0.08 ]

= $ 1,000 * 9.818150

= $ 9,818.15

= $ 9,818    ( When rounded off to the nearest whole number )

Thus if the current Interest rate is 8 %, the present value of the investment paying $ 1,000 for 20 year = $ 9,818

Note: The value of ( 1.08 ) ²⁰   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.08,20) = 4.660957