In 4 years, your son will be entering college and you would like to help financially. You decide to create a college fund and make four annual deposits, starting now. In four years, you would like your son to be able to make four annual withdrawals of $7,500 from the fund (at the beginning of each year) that will cover his annual tuition. If the college fund earns 3.6% compounded annually, how much must you deposit at the beginning of each year? Assume tuition remains the same for the four years your son is attending college.
Make a time graph, marking 'now', yr1, yr2, .... yr7
place x at now, yr1, yr2, yr3, 7500 at each of yr4, yr5, yr6, and yr7
Pick the end of yr3 as your focal point
At that point in time , the Amount of the deposits = Present Value of withdrawals
x( 1.036^4 - 1)/.036 = 7500(1 - 1.036^-4)/.035
x( 1.036^4 - 1) = 7500(1 - 1.036^-4)
tell me what you get?
Is your answer reasonable ?
To determine the amount you need to deposit at the beginning of each year, we can use the formula for the future value of an annuity:
FV = PMT * [(1 + r)^n - 1] / r
Where:
FV = Future value of the annuity
PMT = Amount deposited each year
r = Annual interest rate
n = Number of years
In this case, we know that the future value (FV) of the annuity should be equal to $7,500 per year for four years, with an interest rate (r) of 3.6% compounded annually, and a total of four years (n). We want to find the amount deposited each year (PMT).
Substituting the given values into the formula:
$7,500 = PMT * [(1 + 0.036)^4 - 1] / 0.036
Now, we can solve for PMT:
$7,500 * 0.036 = PMT * [(1.036)^4 - 1]
$7,500 * 0.036 = PMT * [1.1516 - 1]
$270 = PMT * 0.1516
Dividing both sides by 0.1516:
PMT = $270 / 0.1516
Using a calculator, we can find:
PMT ≈ $1,779.81
Therefore, you would need to deposit approximately $1,779.81 at the beginning of each year to ensure your son can make annual withdrawals of $7,500 for four years to cover his tuition expenses.