Question

jack and jill have just had their first child. if college is expected to cost ​$ per year in ​years, how much should the couple begin depositing annually at the end of the next years to accumulate enough funds to pay 1 year of tuition years frm​ now? assume that they can earn a ​% annual rate of return on their investment.

Answer 1

To accumulate enough funds to pay for 1 year of college tuition in n years, Jack and Jill should begin depositing a certain amount annually. We can use the compound interest formula to calculate the required annual deposit.

Step-by-step explanation:

To calculate how much Jack and Jill should begin depositing annually at the end of the next n years, we can use the compound interest formula. The formula is FV = PV * (1 + r)^n, where FV is the future value, PV is the present value (the amount they want to accumulate), r is the annual rate of return, and n is the number of years. In this case, the present value is the cost of 1 year of college tuition, and the future value is the accumulated amount Jack and Jill need to save. Let's say the cost of 1 year of college tuition is $C, the number of years is n, and the annual rate of return is r. Therefore, the formula becomes FV = C * (1 + r)^n. To find how much they need to save annually, we can rearrange the formula to solve for the annual deposit: Annual Deposit = FV / [(1 + r)^n - 1].