Suppose that a young couple has just had their first baby and they wish to ensur

Question

Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child’s college education. The couple expects tuition, books and living expenses to cost $60,000 per year in their child’s first year, and to increase at 4% per year for four years. Assume college payments are made at the end the year (i.e. the freshman payment is made at the end of freshman year, etc.) and that the baby will start college on her 18th birthday.

a) Assuming college savings are invested in an account paying 7% interest, then what is the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education if the parents don’t want to save any more after her 18th birthday?

b) The couple plans to start saving at the end of the year (i.e. on the child’s first birthday) and to save through the 18th birthday. How much do they need to save every year to have enough money in 18 years to pay for college? (they will not save any more after the 18th birthday)

c) If the couple plans to make one savings deposit every TWO years, starting on the child’s second birthday and ending on her 18th birthday, how much will they need to save every two years?

Explanation / Answer

Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child’s college education. The couple expects tuition, books and living expenses to cost $60,000 per year in their child’s first year, and to increase at 4% per year for four years. Assume college payments are made at the end the year (i.e. the freshman payment is made at the end of freshman year, etc.) and that the baby will start college on her 18th birthday.

a) Assuming college savings are invested in an account paying 7% interest, then what is the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education if the parents don’t want to save any more after her 18th birthday?

Amount of money she will need to have available at age 18 = 60000/1.07 + 60000*1.04/1.07^2 + 60000*1.04^2/1.07^3 + 60000*1.04^3/1.07^4

Amount of money she will need to have available at age 18 = $ 215,041.01

b) The couple plans to start saving at the end of the year (i.e. on the child’s first birthday) and to save through the 18th birthday. How much do they need to save every year to have enough money in 18 years to pay for college? (they will not save any more after the 18th birthday)

Amount needed to be Saved each year = pmt(rate,nper.pv,fv)

Amount needed to be Saved each year = pmt(7%,18,0,215041.01)

Amount needed  to be Saved each year = $ 6324.92

c) If the couple plans to make one savings deposit every TWO years, starting on the child’s second birthday and ending on her 18th birthday, how much will they need to save every two years?

Two Year rate = (1+7%)^2 - 1 = 14.49%

Amount needed to be Saved each two year = pmt(rate,nper.pv,fv)

Amount needed  to be Saved each two year = pmt(14.49%,9,0,215041.01)

Amount needed  to be Saved each two year = $ 13092.58

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.