Question

Robert purchased a 2010 model sedan for $16,000. The dealership offered

him a $99/month payment for 60 months, after which the unpaid balance is
due. If the interest rate is 6%, find the balloon payment due at the end of 60
months.
O
A. $17,513.12
O
B. $15,000
C. $18,153.21
O
D. $14,674.37​

Answer 1

The correct option is D. $14,674.37​.

Explanation:

This can be calculated using the ballon payment formula as follows:

P = (PV - (Ballon / (1 + r)^n)) * (r / (1 – (1 + r)^-n)) ...................... (1)

Where:

P = Monthly payment = $99

PV = present value of the loan or the purchase price of the 2010 model sedan = $16,000

Ballon = Ballon payment due at the end of 60 months = ?

r = monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005

n = number of periods or months = 60

Substituting the values into equation (1) and solve for Ballon, we have:

$99 = ($16,000 - (Ballon / (1 + 0.005)^60)) * (0.005 / (1 -(1 + 0.005)^-60))

$99 = ($16,000 - (Ballon / 1.3488501525493)) * 0.0193328015294284

$99 / 0.0193328015294284 = ($16,000 - (Ballon / 1.3488501525493))

$5,120.83051436193 = $16,000 - (Ballon / 1.3488501525493)

Ballon / 1.3488501525493 = $16,000 - $5,120.83051436193

Ballon / 1.3488501525493 = $10,879.1694856381

Ballon = $10,879.1694856381 * 1.3488501525493

Ballon = $14,674.3694203126

Rounding to 2 decimal places, we have:

Ballon = $14,674.37

Therefore, the correct option is D. $14,674.37​.