Final answer:
To ensure the child can withdraw $14,700 per year when they turn 19, we use the present value annuity formula to find the lump sum needed to deposit three years from now. The correct amount is $28,777.49, which will grow at a 6.62% interest rate, compounded semi-annually.
Step-by-step explanation:
The question is asking for the present value of an annuity due to the fact that the withdrawals start immediately after the child turns 19.
Using the formula for the present value of an annuity, which involves the interest rate, the number of periods, and the amount to be withdrawn, we can set up the equation to solve for the present value (PV) required:
PV = PMT [1 - (1 + r)^-n] / r
Where PMT is the payment amount per period, r is the interest rate per period, and n is the number of periods.
However, since we are dealing with a situation where the interest is compounded semi-annually and the payment is annual, we will need to adjust the formula to match the terms.
The correct deposit amount three years from now can be calculated by discounting the annuity's present value back to the deposit time using the formula for compound interest.
Given that the interest rate is 6.62% compounded semi-annually, we need to calculate the present value of $14,700 per year for four years starting from when the child turns 19, and then find the equivalent lump sum amount three years from now that would grow to match that present value.
After solving the equation, Option B is the correct amount to deposit three years from now: $28,777.49.