9-22 Your rich godfather has offered you a choice of one of the three following alternatives: $10,000 now; $2,000 a year for eight years; or $24,000 at the end of eight years. Assuming you could earn 11 percent annually, which alternative should you choose? If you could earn 12 percent annually, would you still choose the same alternative?

Option 1
$10,000 now with a 11% interest.
$10,000 x 11% = $11,100(10,000 + 1,100)
1,100 x 8 yrs = $8,800 + $10,000 = $18,800

$10,000 now with a 12% interest.
$10,000 x 12% = $11,200 (10,000 + 1,200)
1,200 x 8 yrs = $ 9,600 + 10,000 = $19,600

Option 2
$2,000 a year for eight years.

$2,000 x 11% = $2,220
$2,220 x 8 Years = $17,760

$2,000 x 12% = $2,240
$2,240 x 8 Years = $17,920

Option 3
$24,000 at the end of eight years.

Choice: Option 3. The rate of return in Options 1 and 2 is less than what is offered in option 3 at the end of eight years

9-23 You need $28,974 at the end of nine years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year.

a. What single payment could be made at the beginning of the first year to achieve this objective?

A) is a present value question. On a business calculator:

N: 10
i: 8%
FV (future value): -$28,974

will give you a PV of $13,420.57

b. What amount could you pay at the end of each year annually for 10 years to achieve this same objective?

is an annuity problem:

N: 10
i: 8%
FV: -28,974

will give you a yearly payment of $2000.06