Question

Compute the requested value(s) for each scenario. Show all component numbers that factor into determination of the final answer(s) in separate cells. a. You have determined that $120,000 will be required 18 years from now to help pay for your daughter’s higher education. If your bank is paying 6.25% annual rate of return on its ‘College Opportunity’ account, how much must you deposit each quarter to reach your goal?

Answer 1

The formula to calculate the quarterly deposit needed to acquire $120,000 in 18 years with an annual interest rate of 6.25% is the future value of an annuity formula. This is calculated by solving for the Deposit in the formula, based on the annual interest rate, the compounding frequency, and the number of years.

Step-by-step explanation:

Calculating Quarterly Deposits for College Savings

To calculate the amount needed to be deposited each quarter so that you will have $120,000 after 18 years with a 6.25% annual return, we use the future value of an annuity formula:

Future Value = Deposit × ((1 + r/n)^(nt) - 1) / (r/n), where r is the annual interest rate, n is the number of times interest is compounded per year, t is the number of years, and Deposit is the quarterly deposit.

In this case, r = 6.25% (or 0.0625 as a decimal), n = 4 (since interest is compounded quarterly), and t = 18. Rearranging the formula to solve for the deposit gives us:

Deposit = Future Value / (((1 + r/n)^(nt) - 1) / (r/n))

Now, you substitute the given values and calculate the required quarterly deposit to reach the $120,000 goal.