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?

k

step-by-step explanation:

domit

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1