The day your child is born you decide that on each birthday (beginning at the fi

Question

The day your child is born you decide that on each birthday (beginning at the first birthday) you're going to put money away for the child's college tuition. The money will be put in a special education account that pays 5% annually. Tuition today is $25,000 per year. Education experts estimate that over the next 25 years higher education costs will increase at an average annual rate of 2% per year. How much money must you deposit in the education account every year so that at the end of the 18th year there will be sufficient funds on deposit to pay for four years of college without making any further deposits?

Explanation / Answer

First of all let us compute the cost of education 18 years from now. This can be done using the future value formula which is

FV = PV*(1+r)^n = 25000*1.02^18 = $35,706.16

Now the annual deposits that we make should equal to this amount at the end of 18 years with the discount rate to be used as 5%..

So using the formula for future value of annuity we can find the amount of annuity

as

FV = A * [ ((1 + r)^t) - 1] x 1/ r

35706.16 = A * (1.05^18 - 1 ) * 1/0.05

A = $1269.22

FV = A * FVFA(5%, 18 years)

A = FV / FVFA(5%, 18 years)

A = 35706.16 / 28.1324 = $1269.22

So this is the amount that you need to deposit every year to fund your child's college education

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