Multiple Choice Question On January 1, Vango, Inc. purchased a van and promised to pay \( \$ 11,223.34 \) on December 31 for the next 3 years. The market rate of interest is \( 6 \% \) compounded annually. The amount of the purchase is calculated by - multiplying \( \$ 11,223.34 \) by the present value of a \( \$ 1 \) with \( n=3 \) and \( i=6 \% \). dividing \( \$ 11,223.34 \) by the present value of a \( \$ 1 \) with \( n=3 \) and \( i=6 \% \). dividing \( \$ 11,223.34 \) by the present value of an annuity with \( n=3 \) and \( i=6 \% \). multiplying \( \$ 11,223.34 \) by the present value of an annuity with \( n=3 \) and \( i=6 \% \).

To determine how the amount of the purchase is calculated, we need to analyze the payment structure and the present value concepts involved. 1. **Understanding the Payment Structure**: Vango, Inc. is making a series of payments of \( \$ 11,223.34 \) at the end of each year for 3 years. This is an annuity because it consists of equal payments made at regular intervals. 2. **Present Value of an Annuity**: The present value of an annuity formula is used to calculate the current worth of a series of future payments. The formula is given by: \[ PV = P \times \left( \frac{1 - (1 + i)^{-n}}{i} \right) \] where: - \( PV \) = Present Value of the annuity - \( P \) = Payment amount per period - \( i \) = Interest rate per period - \( n \) = Number of periods 3. **Calculating the Present Value**: In this case, we want to find the present value of the annuity that consists of three payments of \( \$ 11,223.34 \) at an interest rate of \( 6\% \). 4. **Options Analysis**: - **Multiplying \( \$ 11,223.34 \) by the present value of a \( \$ 1 \)**: This is incorrect because we are dealing with an annuity, not a single payment. - **Dividing \( \$ 11,223.34 \) by the present value of a \( \$ 1 \)**: This is also incorrect for the same reason. - **Dividing \( \$ 11,223.34 \) by the present value of an annuity**: This is incorrect because we need to multiply the payment by the present value factor, not divide. - **Multiplying \( \$ 11,223.34 \) by the present value of an annuity**: This is correct because we need to find the present value of the total payments by multiplying the payment amount by the present value factor of the annuity. Thus, the correct answer is: **Multiplying \( \$ 11,223.34 \) by the present value of an annuity with \( n=3 \) and \( i=6\% \).**