Darth Vader wants to save money (even Sith Lords needs to be financially savvy!) to meet three objectives:

First, he would like to be able to retire 30 years from now with retirement income of 17,500 imperial credits per month for 25 years, with the first payment received 30 years and 1 month from now.

Second, he would like to build a castle on Mustafar in 10 years at an estimated cost of 345,000 imperial credits.

Third, after receiving the retirement payments for 25 years, he would live to leave an inheritance of 2 million imperial credits to his grandson Kylo Ren.

He can afford to save 2,350 imperial credits per month for the next 10 years. If he can earn an EAR of 10 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in Years 11 through 30?

Amount needed in 10 Year for castle = 345000

Amount needed at retirement for retirement Income and Inheritance amount= Monthly Retirement Income x (1-1/(1+r)^n)/r +Inheritance Value/(1+r)^n

• r (monthly rate) = (1+7%)^(1/12)-1 = 0.56541454%
• n = 25*12 = 300

Amount needed at retirement for retirement Income and Inheritance amount= 17500*(1-1/(1+0.56541454%)^300)/0.56541454% + 2000000/(1+0.56541454%)^300

Amount needed at retirement for retirement Income and Inheritance amount= 2,893,307.74

Monthly Rate  before he retires = (1+EAR)^(1/12)-1

Monthly Rate  before he retires = (1+10%)^(1/12)-1

Monthly Rate  before he retires = 0.797414%

From  saving 2,350 imperial credits per month for the next 10 years

Amount Accumulated at 10 Year time = Monthly Saving x ((1+r)^n-1)/r

• r= 0.797414%
• n = 10*12 = 120

Amount Accumulated at 10 Year time = 2350*((1+0.797414%)^120-1)/0.797414%

Amount Accumulated at 10 Year time = 469680.05

Net Amount needed at 10 Year time = Amount needed in 10 Year for castle + Horizon value of Amount needed at retirement for retirement Income and Inheritance amount in 10 year time - Amount Accumulated at 10 Year time from monthly Saving

Net Amount needed at 10 Year time = 345000 + 2893307.74/(1+0.797414%)^240 - 469680.05

Net Amount needed at 10 Year time = 305391.75

He have to save each month in Years 11 through 30 = Net Amount needed at 10 Year time /((1-1/(1+r)^n)/r)

• r = 0.797414%
• n = (30-10)*12 = 240

He have to save each month in Years 11 through 30 = 305391.75/((1-1/(1+ 0.797414%)^240)/ 0.797414%)

He have to save each month in Years 11 through 30 = 2860.42