You have just had your 30th birthday. You have two children, one of which will g

Question

You have just had your 30th birthday. You have two children, one of which will go to college 10 years from now and require four beginning-of-the-year payments for college expenses of $10,000, $11,000, $12,000, and $13,000. Your second child will go to college 15 years from now and require four beginning-of-the-year payments for college expenses of $15,000, $16,000, $17,000, and $18,000. In addition, you plan to retire in 30 years. You want to be able to withdraw $50,000 per year (at the end of each year) from an account throughout your retirement. You expect to live 20 years beyond retirement. The first withdrawal will occur on your 61st birthday. What equal, annual, and end-of-the-year amount must you save for each of the next 30 years to meet these goals, if all savings earn a 13% annual rate of return? How do I do this on a financial calculator?

Explanation / Answer

In such problem, you need to find present value of deposits and withdrawals and make them equal.

PV of college fee of 1st child:

PV = 10,000/1.13^10 + 11,000/1.13^11 + 12,000/1.13^12 + 13,000/1.13^13

PV = 11236.17

Using TI BA II Plus Pro Calculator

Press CF and input cash flows

CF0 = 0

C01 = 0, F01 = 9

C02 = 10,000, F02 = 1

C03 = 11,000, F03 = 1

C04 = 12,000, F04 = 1

C05 = 13,000, F05 = 1

Now, press NPV and feed I = 13

Scroll when displays NPV press CPT for compute it will display 11,236.17

PV of college fee of 2nd child:

PV = 15,000/1.13^15 + 16,000/1.13^16 + 17,000/1.13^17 + 18,000/1.13^18

PV = 8785.63

PV retirement withdrawal:

PV (60th birthday) = (50,000/0.13)*(1 – 1/1.13^20)

PV (30th birthday) = (50,000/0.13)*(1 – 1/1.13^20)/1.13^30 = 8979.41

Total money required today (30th birthday):

Total PV = 11236.17 + 8785.63 + 8979.41 = 29001.21

Deposits from 31st birthday to 60th birthday

PV = 29001.21, N = 30, r = 13%, FV = 0; compute PMT =?

Use your calculator or formula

29001.21 = (PMT/0.13)*(1 – 1/1.13^30) = 7.495653 PMT

PMT = 3869.07

Required annual saving/deposit = $3869.07

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