$9,234.97 less

Future value = $30,000 x (1 + .055)^38+1 = $242,084.61

Present value = $242,084.61 x [1/(1 + .065)^38+1] = $20,765.03

Difference = $30,000 - $20,765.03 = $9,234.97

CALCULATOR

Enter N: 39, I/Y: 5.5, PV: -30,000, CPT FV --> 242,084.61

Enter N: 39, I/Y: 6.5, FV: 242,084.61, CPT PV --> -20,765.03 $31,662.08

Present value = $1,200,000/(1 + .09)35 = $58,783.28

Present value = $1,200,000/(1 + .09)30 = $90,445.36

Difference = $90,445.36 - 58,783.28 = $31,662.08

(EXAMPLE: When you retire 40 years from now, you want to have $1.2 million. You think you can earn an average of 12 percent on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum 2 years from today. How much more will you have to deposit as a lump sum if you wait for 2 years before making the deposit?

$3,280.78

Present value = $1,200,000 x [1/(1 + .12)^40] = $12,896.16

Present value = $1,200,000 x [1/(1 + .12)^38] = $16,176.94

Difference = $16,176.94 - $12,896.16 = $3,280.78

CALCULATOR

Enter N: 40, I/Y: 12, FV: 1,200,000, CPT PV --> -12896.16

Enter N: 38, I/Y: 12, FV: 1200000, CPT PV --> -16,176.94) ;