Need $28,974 at the end of the 10 years, and theonly 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.

(1) what single payment could be made at the beginning of the first year to achieve this objective?

(2) what amount could you pay at the end of each year annually for 10 years to achieve this same objective?

(1) Using the Future value of 1 table, at 8% for 10 years, you would need #13,420.57 up front.
$13,420.57 x 2.15892 (FV of $1 @ 8% for 10 periods) = $28,974.34
(2) Using the Future value of an Annuity of $1 at 8% for 10 years, you would need to contribute $2,000/yr.
See calc below for proof
Yr Beg Bal Pmt @ Rate on End Bal
Yr End Beg Bal
1 - 2,000.00 2,000.00
2 2,000.00 2,000.00 1.08 4,160.00
3 4,160.00 2,000.00 1.08 6,492.80
4 6,492.80 2,000.00 1.08 9,012.22
5 9,012.22 2,000.00 1.08 11,733.20
6 11,733.20 2,000.00 1.08 14,671.86
7 14,671.86 2,000.00 1.08 17,845.61
8 17,845.61 2,000.00 1.08 21,273.26
9 21,273.26 2,000.00 1.08 24,975.12
10 24,975.12 2,000.00 1.08 28,973.12