Question

2.46

C. More Challenging Problems 2.45 You have just won a lottery prize of $1 000 000 collectable in 10 yearly installments of S100 000 starting today. Why is this prize not really S1 000 0002 What is it really worth today if money can be invested at 10 percent annual interest, compounded monthly? Use a spreadsheet to construct a table showing the present worth of each installment, and the total present worth of the prize. Suppose in Problem 2.45 that you have a large mortgage you want to pay off now. You propose an alternative but equivalent payment scheme. You would like $300 000 today and the balance of the prize in five years when you intend to purchase a large waterfront property. How much will the payment be in five years? Assume that annual interest is 10 percent, compounded monthly. 2.46 piece o

Answer 1

2.46

Effective interest rate R = (1+10%/12)^12 - 1 = 10.47%

Time = 10 years for payment of lottery prize

Yearly payment of prize = $100000

Present value of lottery prize = 100000*(1-1/1.1047^10)/.1 = $630549.33

If $300000 is paid today,

Then,

Remaining lottery amount left for payment = 630549.33-300000 = $330549.33

The value of remaining amount in 5 years = 330549.33*(1+10.47%)^5

The value of remaining amount in 5 years = $543823.6 or $543824