Congratulations! You have been accepted to study gourmet cooking at the Cordon-Bleu Cooking School in Paris.You will need $10,000 every 6 months (beginning today)for the next three years to cover tuition and living expenses.Mom and Dad have agreed to pay for your education,and want to make one deposit today in a bank account earning 6% interest,compounded semi-annually.How much must they deposit now so that you can withdraw $10,000 at the beginning of each semester over the next 3 years?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for present value of an annuity, which is:

PV = (PMT * (1 - (1 + r/n)^(-nt))) / (r/n)

where PV is the present value, PMT is the periodic payment (in this case, $10,000), r is the annual interest rate (6%), n is the number of times the interest is compounded per year (2 for semi-annual compounding), and t is the number of years (3).

Substituting the values, we get:

PV = ($10,000 * (1 - (1 + 0.06/2)^(-2*3))) / (0.06/2)
PV = $55,797.09

So, Mom and Dad need to deposit $55,797.09 today to cover your expenses for the next three years. Therefore, the best choice is B.

Congratulations! You Have Been Accepted to Study Gourmet Cooking at the Cordon-Bleu