A perpetuity costs 77.1 and makes annual payments at the end of the year. The perpetuity pays 1 at the end of year 2, 2 at the end of year 3, ..., n at the end of year (n+1). After year (n+1), the payments remain constant at n. The annual effective interest rate is 10.5%. Calculate n.

Since it pays 1 at end of year 2 and increases by 1 til end of year (n+1), I did

(a(double dot angle n+1) * v) / 0.105 = 77.1

When I do this i get n = 18 and I am off by 1 from the correct answer n = 19.

Can someone point out my error here?

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

i think you would have to divide the money he had saved, which is $2,000 by the time he plans on exercising which is 40 hours, and the answer you get should tell you the answer to your question.