Question

Peggy has two children, Kelly age 6, and Kirsten age 3. Susan wants to provide for their education funding. Currently, tuition is $10,000 per year and tuition inflation is 9%. Peggy expects to earn 11% on her investments and she expects the children to start college at age 18 and go to college for 5 years. Peggy wants her last savings payment to be made when the oldest child starts college. How much must Peggy save at the end of each year? (Hint: use the uneven cash flow method)

Answer 1

Okay, here are the steps to solve this problem using the uneven cash flow method:

1) Identify the key inputs:

- Tuition today: $10,000 per year

- Tuition inflation: 9% per year

- Expected investment return: 11% per year

- Children's ages: Kelly (6), Kirsten (3)

- College duration: 5 years

- Last savings payment when oldest (Kelly) starts college at age 18

2) Calculate future tuition amounts:

Year 1 (age 7): $10,000 * (1.09) = $10,900

Year 2 (age 8): $10,900 * (1.09) = $11,881

Year 3 (age 9): $11,881 * (1.09) = $12,914

Year 4 (age 10): $12,914 * (1.09) = $14,048

Year 5 (age 11): $14,048 * (1.09) = $15,252

Year 6 (age 12): $15,252 * (1.09) = $16,531

Year 7 (age 13): $16,531 * (1.09) = $18,042

Year 8 (age 14): $18,042 * (1.09) = $19,626

Year 9 (age 15): $19,626 * (1.09) = $21,289

Year 10 (age 16): $21,289 * (1.09) = $23,062

Year 11 (age 17): $23,062 * (1.09) = $25,007

Year 12 (age 18): $25,007

3) Calculate total tuition cost:

Year 1 to 5 (Kelly): $10,900 + $11,881 + $12,914 + $14,048 + $15,252 = $65,995

Year 6 to 10 (Kirsten): $16,531 + $18,042 + $19,626 + $21,289 + $23,062 = $98,550

Year 11 to 12 (both): $25,007 + $25,007 = $50,014

Total tuition cost = $65,995 + $98,550 + $50,014 = $214,559

4) Calculate annual savings amount to meet total cost:

$214,559 / 12 years = $17,880 (last payment at age 18)

So the annual amount Peggy must save is $17,880.

Let me know if you have any other questions!