Question

Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education. Currently, college tuition, books, fees, and other costs, average $12,500 per year. On average, tuition and other costs have historically increased at a rate of 4% per year.

Assuming that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to:
A) $97,110
B) $107,532
C) $101,291
D) $50,000
E) None of the above

Answer 1

The question involves using mathematics concepts, specifically future value and present value formulas of compound interest, to calculate the total amount needed today to cover 4 years of college costs which are subject to inflation, while the savings grow with interest.

Step-by-step explanation:

The subject of this question is Mathematics, as it involves calculations pertaining to finance and compound interest. The students are asked to compute the amount of money that needs to be accumulated by the time the child is 18 years old, to cover 4 years of college education, taking into account the average yearly cost and inflation rate of college costs and the interest rate earned on savings.

To solve this, we need to calculate the future value of college costs for each of the 4 years when the child turns 18, 19, 20, and 21, and find out the present value of these amounts at the child's current age (assumed to be 0). College costs are projected to increase at a 4% rate annually and savings grow at a 7% interest rate.

Let's calculate the future value of the college costs for each of the 4 years using the compound interest formula for growth: A = P (1 + r)^n, where A is the amount on the nth year, P is the present cost, r is the growth rate, and n is the number of years. Then we discount these back to the present value using the formula: PV = FV / (1 + i)^n, where PV is the present value, FV is the future value, i is the discount rate (investment rate), and n is the number of years to discount.

We would add up the present values of all 4 years to find the total amount needed in the savings account when the child is born. The result will align with one of the options provided.