Final answer:
To have $13,500 in 7 years at an effective annual interest rate of 6%, you would need to invest approximately $8,971.89 today.
Step-by-step explanation:
To calculate how much you would need to invest today to have $13,500 in 7 years at an effective annual interest rate of 6%, we can use the formula for the present value of a single future sum, which is:
PV = FV / (1 + r)^n
Where:
- PV is the present value (the amount you need to invest today)
- FV is the future value (the $13,500)
- r is the annual interest rate (6% or 0.06)
- n is the number of years (7)
Plugging the numbers into the formula yields:
PV = $13,500 / (1 + 0.06)^7
PV = $13,500 / (1.06)^7
PV = $13,500 / 1.5036
PV = $8,971.89
Therefore, you would need to invest approximately $8,971.89 today to have $13,500 in 7 years at an effective annual interest rate of 6%.