An annuity provides for 30 annual payments. The first payment of 100 is made immediately and the remaining payments increase by 8 percent per annum. Interest is calculated at 13.4 percent per annum. Calculate the present value of this annuity.

$1423.38

Explanation:

number of payments ( number of years )(n) = 30

first payment = $100

interest calculated at : 13.4 % = 0.134

increment rate : 8 percent = 0.08

we can calculate the present value using this Equation

= (p / (r-g))  * [1 - [(1+g)/(1+r)]^n ]

where :

p / (r-g) = 100 / (0.134 - 0.08 ) = $1852

[1 - ((1+g)/(1+r)]^n ) =  (1 - ((1.08/1.134)^30 ) =  0.7686

hence the present value of this annuity = $1852 * 0.7686 = $1423.38

Note :

p ( first principal payment ) = $100

r ( calculated interest ) = 13.4% = 0.134

g ( increment interest ) = 8 % = 0.08