Question

5. What is the future value of a 5-year ordinany annuity with annual payments. of 1250, evaluated at a 15 % interest Irate ?

Answer 1

Solution:

The formula for calculating the Future value of ordinary annuity at the end of n years is

= P *[ [ ( 1 + r ) ⁿ- 1 ] / r ]

Where P = Periodic Payment i.e., Fixed amount of Annual payment

r = rate of interest   ; n = no. of years

A per the information given in the question we have

P = $ 250    ; r = 15 % = 0.15   ;   n = 5

Applying the above values in the formula we have:

= 250 * [ [ ( 1 + 0.15 ) ⁵   - 1 ] / 0.15 ]                             

= 250 * [ [ ( 1.15 ) ⁵   - 1 ] / 0.15 ]

= 250 * [ [ 2.011357 – 1 ] / 0.15 ]

= 250 * [ 1.011357 / 0.15 ]

= 250 * 6.742380

= 1,685.595000

= $ 1,685.60 ( when rounded off to two decimal places )

Thus the future vale of the 5 year annuity is = $ 1,685.60

Note: The value of ( 1.15 ) ⁵   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.15,5)= 2.011357