Final answer:
To reach a goal of $18,000 in 4 years with a monthly interest rate of 0.325%, you would need to invest approximately $15,762.79 today. We use the present value formula for compound interest to calculate this amount.
Step-by-step explanation:
To determine how much needs to be invested today to achieve a future goal of $18,000 in 4 years with a monthly interest rate of 0.325%, we use the formula for the present value of a future amount in compound interest situations. The formula is as follows:
PV = FV / (1 + r)^n
Where:
PV is the present value, or the amount to be invested today.
FV is the future value, or the amount needed in the future ($18,000).
r is the monthly interest rate (0.325% or 0.00325 as a decimal).
n is the total number of compounding periods (4 years * 12 months/year = 48 months).
Plugging the values into the formula, we get:
PV = $18,000 / (1 + 0.00325)^48
Calculating this out, we find:
PV = $18,000 / (1.00325)^48
After computing the expression in the denominator and dividing it into $18,000:
PV ≈ $15,762.79
Therefore, you would need to invest approximately $15,762.79 today to have $18,000 in 4 years, assuming a 0.325% monthly rate of compound interest.