Final answer:
To determine the total available funds for the Jenkins family fun center in four years, one must calculate the future values of each separate deposit using the formula for compound interest and then sum those values. The correct computation should carefully apply the 8 percent rate of return over the appropriate number of years for each deposit.
Step-by-step explanation:
The Jenkins family fun center is interested in calculating the future value of their investment account to buy new equipment in the future. They are making periodic deposits and the account earns an 8 percent rate of return. To compute the future value of three separate deposits, we will use the future value formula for compounding interest, which is FV = PV(1 + r)n, where FV is the future value, PV is the present value, r is the rate of return per period, and n is the number of periods.
- For the initial deposit made one year ago ($4,500): FV = $4,500 * (1 + 0.08)5 (since we are looking 4 years from today, and it was deposited a year ago, we have 5 years total).
- For the deposit made today ($6,300): FV = $6,300 * (1 + 0.08)4 (4 years from today).
- For the deposit that will be made next year ($8,500): FV = $8,500 * (1 + 0.08)3 (three years from the time of deposit).
Calculate each future value separately and then sum them up to get the total amount available when they are ready to buy the equipment.
It's important to note that any deviation from the correct formula or method of computing the future value will lead to an incorrect answer, so one must ensure all the calculations are done accurately to arrive at the right total available in the account.