To determine the amount of each annual payment needed to accumulate $97,703 in 15 years with an interest rate of 3.15% compounded annually, we can use the formula for the future value of an ordinary annuity.
The formula is:
Future Value = Payment × [(1 + Interest Rate)^(Number of Periods) - 1] / Interest Rate
In this case, the future value is $97,703, the interest rate is 3.15%, and the number of periods is 15.
Let's calculate the annual payment:
$97,703 = Payment × [(1 + 0.0315)^(15) - 1] / 0.0315
To simplify the equation, we can first calculate the expression inside the brackets:
(1 + 0.0315)^(15) = 1.6031
Now, let's substitute this value back into the equation:
$97,703 = Payment × (1.6031 - 1) / 0.0315
To isolate the Payment, we can multiply both sides of the equation by 0.0315:
Payment × (1.6031 - 1) = $97,703 × 0.0315
Simplifying further:
Payment × 0.6031 = $3,077.8455
Finally, divide both sides by 0.6031 to solve for Payment:
Payment = $3,077.8455 / 0.6031
Payment ≈ $5,107.65 (rounded to the nearest cent)
Therefore, each annual payment would need to be approximately $5,107.65 in order to accumulate $97,703 for your son's education in 15 years, assuming a 3.15% annual interest rate compounded annually.