Question

A man begins setting aside money for a child's college expenses, sadly due to rises in tuition there really isn't much room for a graduation gift. What should the value of the annuity be if he begins depositing on year 1 and deposits a total of 15 annuities at 6.1%. The child will draw 9835 dollars at year 18 since they have scholarships, 15203 dollars on years 19 and 20 since they have lost their scholarships, and 19888 dollars on year 21 since they are in excess credit hours and have changed their major from engineering to communications. Afterwards, the parents can be considered to have no more money to give said child. He or she is now left to deal with predatory student loan companies since America has done little in the way subsidizing higher education.

Answer 1

Answer:

Let us assume deposit starts on start of year 1.

Total of 15 annual deposits are made.

Rate of interest = 6.1%

Withdrawals:

1. At the start of year 18 = $9,835

Value at the start of year 16 will be = Future Value / (1 + Interest rate) ⁿ = $9,835 /(1 + 6.1%)²

2. At the start of year 19 = $15,203

Value at the start of year 16 will be = Future Value / (1 + Interest rate) ⁿ = $15,203 /(1 + 6.1%)³

3. At the start of year 20 = $15,203

Value at the start of year 16 will be = Future Value / (1 + Interest rate) ⁿ = $15,203 /(1 + 6.1%)⁴

4.At the start of year 21 = $19,888

Value at the start of year 16 will be = Future Value / (1 + Interest rate) ⁿ = $19,888 /(1 + 6.1%)⁵

As such value of all withdrawals as on start of year 16 = $9835 / (1 + 6.1%) ² + $15,203/ (1 + 6.1%) ³ + $15,203 / (1 + 6.1%) ⁴ + $19,888 / (1 + 6.1%) ⁵

= $48,253.73

Now we can use PMT function of excel to get value of annuity:

PMT (rate, nper, pv, fv, type)

PMT (6.1%, 15, 0, -48253.73, 1)

=$1,939.09

Required value of the annuity = $1,939.09