The present value (PV) of an investment is the amount that should be invested today at a specified interest rate in order to earn a certain amount at a future date. The amount desired is called the future value. For a future value of $10,000, which of the following functions models the present value,PV, to be invested in a savings account earning 5% interest compounded annually for t years?

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Identify Given Values: We need to use the formula for the present value (PV) of an investment with compound interest. The formula is: PV = FV / (1 + r)^t where FV is the future value, r is the annual interest rate (as a decimal), and t is the number of years.Substitute Values into Formula: First, we identify the given values: FV = $10,000 (future value) r = 5% or 0.05 (annual interest rate) t = unknown (number of years) We will express the present value PV as a function of t.Simplify Expression: Now, we substitute the given values into the formula: PV = 10000 / (1 + 0.05)^t This function will give us the present value for any number of years t.Final Present Value Function: We simplify the expression to make it clear: PV = 10000 / (1.05)^t This is the function that models the present value.

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