Find the present value of the following:

a 2:

sh

$5,000 received 8 years from now discounted at 8%.

$10,000 received 5 years from now discounted at 6%.

$8,000 per year (beginning at the end of the first year) for 4 years dis- counted at 12%.

. $4,000 per year (beginning at the end of the first year) for 6 years discounted at 10%.

- $4,000 per year (beginning at the end of the first year) for 3 years followed by $3,000 per year for 5 years, all discounted at 8%.