Final answer:
An investor needs to invest approximately $7,863.97 today at a 5% annual interest rate to have $9,100 at the end of 3 years, as calculated using the present value formula.
Step-by-step explanation:
To determine how much an investor needs to invest today to have $9,100 at the end of 3 years with an interest rate of 5%, we need to calculate the present value of the future amount. This is done using the formula for the present value of a single future amount, which is:
PV = FV / (1 + r)^n,
where:
PV = Present Value (the amount to invest today),
FV = Future Value (the amount the investor wants to have in the future, which is $9,100),
r = interest rate per period (5% or 0.05 as a decimal), and
n = number of periods (3 years).
Using the formula, we get:
PV = $9,100 / (1 + 0.05)^3
= $9,100 / (1.157625)
≈ $7,863.97.
Therefore, the investor needs to invest approximately $7,863.97 today to have $9,100 in 3 years at a 5% annual interest rate.