Question

annuity A makes annual payment of R1200 for each of the next 10 years while annuity B makes R750 per year forever at what interest rate would you be indifferent

Answer 1

A:

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

=$1200[1-(1+interest rate)^-10]/interest rate

B:

Present value of perpetuity=Annual flows/interest rate

=$750/interest rate

Hence

$1200[1-(1+interest rate)^-10]/interest rate =$750/interest rate

$1200[1-(1+interest rate)^-10] =$750

1-(1+interest rate)^-10=(750/1200)

1-(750/1200)=(1+interest rate)^-10

0.375=[1/(1+interest rate)]^10

(0.375)^(1/10)=[1/(1+interest rate)]

0.906573722=1/(1+interest rate)

1+interest rate=1/0.906573722

interest rate=1.103054253-1

=10.31%(Approx)