Question

You are buying a perpetuity with annual payments as follows Payment of X at the end of the first year and every three years thereafter. Payment of X+1 at the end of the second year and every three years thereafter. Payment of X+2 at the end of the third year and every three years thereafter The interest rate is 5% convertible semi-annually. If the present value is 40, Calculate

Calculate X

Answer 1

The payments are x,x+1,x+2,x,x+1,x+2......

Here find the value at t = 3 of the above mentioned payments.

Thus x(1.025^4) + (x+1)(1.025^2) + (x+2) will be the effective payment every 3 years.

Effective interest rate = (1.025^6)-1

Thus x(1.025^4) + (x+1)(1.025^2) + (x+2)/(1.025^6) -1 = 40

Thus solving the above equation we get x = 1.05791.

This can be rounded off to 2 decimal places and so x = 1.06