Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Victor wants to purchase a perpetuity paying 100 per year with the first payment due at the end of year 11. He can purchase it by either: (i) paying 90 per year at the end of each year for 10 years; or i) payıng K per year at the end of each year for the years and nothing for the next 5 years. Calculate K

Sagot :

Manetho

Answer:

K = 151.9422481

Step-by-step explanation:

At the end of year 10, your perpetuity is worth 100/i

(1) is worth 90×s_{10%i}

So if you set them equal you get 90*[(1+i)^10 - 1]/i = 100/i or [(1+i)^10 - 1] = 10/9 or (1+i)^10 = 19/9 or i = 0.077583937

So now the question compare (1) to (2), at t = 0

(1) is worth 90×a_{10%i} = 90(1 - 1/(1.077583937)^10)/0.077583937 = 610.5441743

(2) is worth K×a_{5%i} = 4.018264714×K

Therefore K = 151.9422481

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.