Question

Denzel needs a new car. At the dealership, he finds the car that he likes. The dealership gives him two payment options:

1. Pay $35,000 for the car today.

2. Pay $4,000 at the end of each quarter for three years.


Assuming Denzel uses a discount rate of 12% (or 3% quarterly), calculate the present value. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Round your answers to 2 decimal places. )

Answer 1

To calculate the present value, we discount each payment using the appropriate discount rate. For option 1, where Denzel pays $35,000 today, the present value is simply $35,000. For option 2, where Denzel pays $4,000 at the end of each quarter for three years, the present value is $11,325.87.

Step-by-step explanation:

To calculate the present value, we need to discount each payment using the appropriate discount rate.

For option 1, where Denzel pays $35,000 today, the present value is simply $35,000 since there are no future payments to discount.

For option 2, where Denzel pays $4,000 at the end of each quarter for three years, we need to determine the present value of each individual payment and sum them up.

Using the formula for Present Value of an Annuity (PVA), which is: PVA = C * ((1 - (1+r)^-n) / r), where C is the payment amount, r is the discount rate per period, and n is the number of periods, we can calculate the present value of each quarterly payment as follows:

For the first year:

1. $4,000 / ((1+0.03)^1) = $3,883.50

For the second year:

1. $4,000 / ((1+0.03)^2) = $3,773.82

For the third year:

1. $4,000 / ((1+0.03)^3) = $3,668.55

Now, we can sum up these present values to find the total present value:

1. $3,883.50 + $3,773.82 + $3,668.55 = $11,325.87

Therefore, the present value for option 2 is $11,325.87.