Final answer:
To reach an $83,000 goal in 9 years with a 0.50% monthly interest rate, you can calculate the present value needed to deposit today using the formula PV = FV / (1 + r)^n. Convert the monthly interest rate to a decimal and calculate based on the 108 compounding periods to find the present value.
Step-by-step explanation:
To find out how much you need to deposit today to reach an $83,000 goal in 9 years with a 0.50 percent monthly interest rate, you can use the formula for the present value of a single future sum with compound interest.The formula is: PV = FV / (1 + r)^nowhere PV is the present value (the amount of money you need to deposit now), FV is the future value (the amount of money you want to have in the future), r is the monthly interest rate (as a decimal), and n is the number of periods the money is compounded (in months).Let's convert the monthly interest rate from a percentage to a decimal: 0.50% = 0.005. The number of periods will be 9 years times 12 months/year = 108 months.Now we can plug the values into the formula:PV = 83000 / (1 + 0.005)^108 Calculating this gives us the present value which is the amount you need to deposit today to reach your goal of $83,000 in 9 years.