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? Choose 1 answer: (A) PV(t)=10,000(1.05)^(t) (B) PV(t)=10,000(1.05)^(-t) (C) PV(t)=10,000(1+0.05 t) (D) PV(t)=10,000(1-0.05 t)

Question

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? Choose 1 answer: (A)  PV(t)=10,000(1.05)^(t) (B)  PV(t)=10,000(1.05)^(-t) (C)  PV(t)=10,000(1+0.05 t) (D)  PV(t)=10,000(1-0.05 t)

Bytelearn · Accepted Answer

Reverse Compound Interest Formula: To find the present value, we need to use the formula for compound interest in reverse, which is PV = FV / (1 + r)^t, where FV is the future value, r is the interest rate, and t is the time in years.Given Values: We are given FV = $10,000, r = 5% or 0.05, and t is the number of years. We need to find the function that represents PV.Substitute Values: Substitute the given values into the formula: PV = 10,000 / (1 + 0.05)^t.Simplify Equation: This simplifies to PV = 10,000 / (1.05)^t, which is the same as PV = 10,000 * (1.05)^(-t).Correct Present Value Function: Looking at the choices, the correct function that models the present value is PV(t) = 10,000 * (1.05)^(-t).

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