Beth & Ed Carlton want to begin some serious financial planning to fund the future education costs

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Question:

Beth & Ed Carlton want to begin some serious financial planning to fund the future education costs of their 3-year old son, Matthew. They assume that Matthew will attend Ed's alma mater, AB College (ABC), beginning 15 years from today. Current tuition at ABC is $11,500 per year. Current room & board costs at ABC are about $6,000 per year.

The only investment Beth & Ed have made to pay for Matthew's college costs are 10 zero-coupon bonds that they purchased when Matthew was born. The face amount of each bond is $1000. The bonds were originally purchased for $490 each with an original maturity of 18 years. They are now scheduled to mature 15 years from today.

The Carlton's have asked you to help them plan for the costs of Matthew's future college education, In your conversations with Beth & Ed, they told you they want to accumulate all the needed funding by the time Matthew enters college so that they can begin to save extra for their retirement while Matthew is in college. They also told you that Ed's father (Jim Carlton) wants to help pay for Matthew's college education.

Questions:

1) If ABC's annual tuition increases by 8% per year, approximately how much will the annual tuition be for Matthew during his freshman year?

2) If ABC's room & board costs increase by 5% per year, what will be the approximate total costs of tuition plus room & board be for Matthew's senior year at ABC?

3) Assume that you estimate the Carlton's will need to pay approximately $218,200 (Year 1 = $49,000, Year 2 = $52,500, Year 3 = $56,300, Year 4 = $60,400) for four years of tuition and room & board while Matthew attends ABC. If the Carlton's earn an after-tax return of 8.5% during Matthew's 4 years in college, how much do they need to have at the start of Matthew's freshman year to fully pay for all 4 years at ABC?

4) Jim Carlton is willing to help accumulate some of the funds needed for Matthew's college costs. Jim is prepared to put a lump sum of $20,000 into an investment account today and make four additional annual deposits of $5,000 each year beginning in one year from today. If the investment account earns a compound annual after-tax rate of return of 4.5%, how much will be in the investment account four years from now (after the last deposit is made)?

5) After evaluating the entire situation, Beth & Ed decide they will try to accumulate the equivalent of $100,000 in today's dollars by the end of 15 years to help pay for Matthew's college costs. They want to do so through 15 annual deposits, starting immediately. The size of each annual deposit will be 5% higher than the previous one. This corresponds with the expected annual inflation rate and annual increase in the Carlton family income during that period. They have decided to place the deposits in a mutual fund you recommended. The compound annual after-tax rate of return from your recommended fund is expected to be 7%. Based on these assumptions, how large should the initial deposit be?