Final answer:
To meet college expenses over the next four years with quarterly withdrawals of $3,400 and a 0.56% interest rate, you would need approximately $302,670.60 in your bank account today.
Step-by-step explanation:
Retirement Account Calculation
To solve for the amount needed today to meet the college expense needs over the next four years, we will use the formula for the present value of an annuity due to the quarterly withdrawals. The formula is PV = PMT × ((1 - (1 + r)^{-n}) / r)× (1+r), where PV is the present value (initial amount needed), PMT is the quarterly withdrawal amount, r is the quarterly interest rate, and n is the total number of withdrawals.
In this scenario, PMT is $3,400, r is 0.56% or 0.0056 in decimal form, and n is 4 years times 4 quarters/year, which equals 16 quarters. Using the formula, we calculate:
- PV = $3,400 × ((1 - (1 + 0.0056)^{-16}) / 0.0056)× (1+0.0056)
- PV = $3,400 × ((1 - (1.0056)^{-16}) / 0.0056)× 1.0056
- PV = $3,400 × ((1 - 1.0056^{-16}) / 0.0056)× 1.0056
- PV = $3,400 × (0.088488211)× 1.0056
- PV = $3,400 × (0.089009)
- PV ≈ $302,670.60
Therefore, you would need approximately $302,670.60 in your bank account today to meet your expense needs over the next four years with a quarterly interest rate of 0.56 percent.