Final answer:
Tom and Erin will need $87,171.30 in their investment account when their child turns 18 to cover 4 years of college tuition estimated at $27,500 per year, assuming a 10% annual return. The present value of the annuity formula is used to calculate this amount, leading to the correct answer C.
Step-by-step explanation:
The student is asking how much money Tom and Erin will need in their investment account when their child Tommie turns 18 to cover college tuition estimated at $27,500 per year for 4 years, assuming an annual investment return of 10%. To solve this, we need to calculate the present value of the total college costs using the formula for the present value of an annuity.
The formula for present value (PV) of an annuity is: PV = PMT [(1 - (1 + r)^-n) / r], where PMT is the annual payment (tuition), r is the annual interest rate, and n is the number of periods (years). In this case, PMT is $27,500, r is 0.10 (10% expressed as a decimal), and n is 4.
We calculate the present value as follows:
PV = $27,500 [(1 - (1 + 0.10)^-4) / 0.10]
PV = $27,500 [(1 - 1/1.4641) / 0.10]
PV = $27,500 [(1 - 0.683013) / 0.10]
PV = $27,500 [0.316987 / 0.10]
PV = $27,500 × 3.16987
PV = $87,171.30
Therefore, Tom and Erin will need $87,171.30 in their account when Tommie turns 18 to cover the cost of college tuition for 4 years, given a 10% annual return on their investment. The correct answer is C. $87,171.30.