Question

Assume the annual interest rate is 6%. Calculate the value of an investment that pays $100 every two years, starting two years from now and continuing forever.

Answer 1

Answer:

To use our formuals, the interest period and the payments periods must be the same, so we have to convert the 6% per annum to a rate compounded every two years.

let that rate be i

(1+i) = 1.06^2 = 1.1236

PV = 100(1.1236)^-1 + 100(1.1236^-2) + ....

a = 100(1.1236^-1) , r = 1.1236^-1 = .8899996...

using sum∞ = a/(1-r)

= 100(1.1236^-1)/.11000356 = 809.06

or, just thought of a simpler way ....

let that amount be x

x(1.06)^2 - 100 = x

x(1.06^2) - x = 100

x(1.06^2 - 1) = 100

x = 100/.1236 = 809.06