As an employee in the Lottery Commission, your job is to design a new prize. Your idea is to create two grand prize choices: (1) receiving $50,000 at the end of each year beginning in one year for 20 consecutive years, or (2) receiving $500,000 today followed by a one-time payment at the end of 20 years. Using an interest rate of 6%, which of the following comes closest to the amount prize (2) needs to pay at the end of year 20 in order that both prizes to have the same present value?

a. $ 326,649

b. $ 440,463

c. $ 114,932

d. $ 393,342

e. $ 235,712

The correct option is $235,712, option E

Explanation:

The present value of prize (1) can be computed by using the excel pv formula as shown below:

=-pv (rate, nper, pmt, fv)

rate is interest rate of 6%

nper is the number of years payment would be made which is 20

pmt is the amount of money received per year which is $50,000

fv is the total future worth of the prize (1) which is unknown

=-pv (6%,20,50000,0)

=$573,496.06

The difference between present value of prize (1) $573,496.06 and $500,000 receivable from prize (2) today is $73,496.06

The difference is today's worth, its future worth can be computed thus:

FV=PV * (1+r) ^n

PV is $73,496.06

r is 6%

n is 20 years

FV=$73,496.06 * (1+6%) ^20 = $ 235,711.82