Question

How much more is a perpetuity of $800 worth than an annuity of the same amount for 38 years? Assume an annual interest rate of 12% and cash flows at the end of each period. Given annual compounding.

a.)$98.86

b.)$89.87

c.)$85.38

d.)$92.57

Answer 1

Present value of perpetuity=Annual cash flows/interest rate

=800/0.12

=$6666.67(Approx)

Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=800[1-(1.12)^-38]/0.12

=800*8.22099347

=$6576.79(Approx)

Hence difference=6666.67-6576.79

=$89.87(Approx)