Question

Susan has just had her 40th birthday. She has two children. One will go to college 8 years from now and require four year beginning-of-year payments for college expenses, $13,000, $13,500, $14,500, and $15,500. The other will go to college 14 years from now and require four year beginning-of-year payments for college expenses, $16,000, $17,500, $19,000, and $20,500. In addition, Susan plans to retire in 20 years. Susan wants to be able to withdraw $75,000 per year (at the end of each year) from an account for 30 years. The first withdraw occurs on her 61st birthday. What equal, annual, end of-year amount must Susan save for each of the next 20 years to meet these goals if all savings earn a 14% annual rate of return? PLEASE SHOW WORK USING FINANCIAL CALCULATOR

Answer 1

Amount required to be withdrawn every year after retirement = 75,000
Rate = 14%
Number of Years = 30
The Value of Retirement fund Required at retirement = 75000*(1-(1+r)^-n)/r = 75000*(1-(1+14%)^-30)/14% = 525,199.81

The PV of retirement fund = 525,199.81/(1+14%)²⁰ = 38,214.443

PV of the college fees of 2 children = 13000/(1+14%)⁸ + 13500/(1+14%)⁹ + 14500/(1+14%)¹⁰​​​​​​​ + 15500/(1+14%)¹¹​​​​​​​ + 16000/(1+14%)¹⁴​​​​​​​ + 17000/(1+14%)¹⁵​​​​​​​ +19000/(1+14%)¹⁶​​​​​​​ + 20500/(1+14%)¹⁷ = ​​​​​​​25,769.315

The PV of all her costs = 38,214.44 + ​​​​​​​25,769.315 = 63,983.757

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The equal annuity savings for 20 years = 63,983.757*(1-(1+r)^-n)/r =  63,983.757*(1-(1+14%)^-20​​​​​)/14% = 9,660.65