Question

Aperpetuity-immediate is designed to pay $5000 at the end of each year for 10 years and then $1000 at the end of each year forever. The annual effective interest rate is 996. Determine a fair purchase price for this annuity. Purchase price = $

Aperpetuity-immediate is designed to pay $5000 at the end of each year for 10 years and then $1000 at the end of each year forever. The annual effective interest rate is 9%. Determine a fair purchase price for this annuity. Purchase price = $

Answer 1

Interest rate = 9.96%

Present value of $5000 at end of each year for 10 years = (5000/9.96%)*(1-1/(1+9.96%)^10) = $30775.5

Value of perpetuity paying $1000 at end of 10 years = 1000/9.96% = 10040.2

Present value of perpetuity = 10040.2/(1+9.96%)^10 = 3885

Purchase price = 30775.5+3885 = $34660.7

Interest rate = 9%

Present value of $5000 at end of each year for 10 years = (5000/9%)*(1-1/(1+9%)^10) = $32088.3

Value of perpetuity paying $1000 at end of 10 years = 1000/9% = 11111.1

Present value of perpetuity = 10040.2/(1+9%)^10 = 4693.5

Purchase price = 30775.5+3885 = $36781.7