Alex meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $70,000 cash immediately, (2) $24,000 cash immediately and a six-period annuity of $8,100 beginning one year from today, or (3) a six-period annuity of $14,500 beginning one year from today. (fv of $1, pv of $1, fva of $1, pva of $1, fvad of $1 and pvad of $1). 1. assuming an interest rate of 7%, determine the present value for the above options.

The net present value for each option is given below.

(1) $70,000 cash immediately

NPV = 70,000 * 1 = $ 70,000

(2) $24,000 cash immediately and a six-period annuity of $8,100 beginning one year from today, or

NPV = (24,000*1) + (8,100 *(1-((1+7%)^-6)/7%)) = $ 62,609

(3) a six-period annuity of $14,500 beginning one year from today

NPV = (14,500 *(1-((1+7%)^-6)/7%)) = $ 69,115

explanation:

the contractual interest rate is the interest the borrower must pay and the interest the lender receives, or more simply, it is the interest rate stated on a bond whereas the market interest rate is “the investors demand for loaning funds”. therefore, bonds can either be sold at a premium, face value, or discount.