11.25 Personal Financial Planning Problem
You are given the following:
- This year, Abraham will start graduate school. The annual cost is $30,000 per year for each of two years, payable at the start of the year.
- The tuition will increase by 3% in the second year, due to inflation.
- Abraham currently owes $25,000 from his undergraduate student loans.
- When he finishes his M.B.A. in two years, his parents will give him a $50,000 gift.
- Upon graduation, Abraham plans to pay off his loans fully in ten years. How much will he have to pay annually in order to achieve his goal?
- Assume throughout an 8% cost of funds rate, compounded quarterly, except for the annuity payoff payments, which will be at an 8% annual rate.
Solution Plan:
- First lay down the given data, in nominal terms, in their proper places in a timeline; then, import the numbers into a spreadsheet.
- Calculate the future value of the costs at the end of year 2, using the cost of funds rate given. Note the gift as money in.
- Use the mortgage formula to calculate the annuity payment required to pay off the accumulated debts in the last 10 years.
Solution:
Calculations:
Step 1: ($30,000) (1 + .08/4) 2 × 4 = $35,149.78
Step 2: $30,000 × 1.03 = $30,900
($30,900) (1 + .08/4) 1 × 4 = $33,447.15
Step 3: $25,000 × (1 + .08/4) 2 × 4 = $29,291.48
Step 4: $50,000 gift
Step 5: Sum of Steps 1-4
Step 6: Calculate the annual annuity payments.
(47,888.41) = (x) (PVAF 0.08; 10)
(47,888.41) (6.7101)
x = 7,136.77