Question

1. What is the PV of a perpetuity of $100 at an interest rate of 6%?

2. What is the PV of a perpetuity of $100 growing at a rate of 2% per year and earning an interest rate of 6%?

3. What is the present value of $100 invested at the beginning of each year at 5% for 6 years?

Answer 1

1. present value value of perpetuity = annual amount / interest rate

=>$100/6%

=>$1,666.67.

2.Present value of a growing perpetuity = $1000 / (6%-2%)

=>1000/4%

=>$25,000.

3.present value of annuity immediate = P + P*[1-(1+r)^-(n-1)]/r

here,

P =100

r=5%=>0.05

n=6

n-1=>5 years.

=>100+100*[1-(1.05)^-5]/0.05

=>100+100*4.329476

=>100+432.9476

=>$532.95.