Question

Word Problem 14-8 (Algo) [LU 14-1 (1, 2))

Before purchasing a used car, Cody Lind checked www.kbb.com to learn what he should offer for the used car he wanted to buy. Then
he conducted a carfax.com search on the car he found to see if the car had ever been in an accident. The Carfax was clean so he
purchased the used car for $14,900. He put $2,300 down and financed the rest with a 48-month, 7.5% loan. What is his monthly car
payment by table lookup? (Use Table 14.2)
Note: Do not round intermediate calculations. Round your answer to the nearest cent.
Monthly payment

Answer 1

Cody Lind's monthly car payment, obtained by table lookup using the amortization formula, is approximately $310.51 for a 48-month, 7.5% loan on the used car.

To find Cody Lind's monthly car payment, we can use the formula for calculating the monthly payment on an amortizing loan, which is given by the formula:

`\[ M = (P \cdot r \cdot (1 + r)^n)/((1 + r)^n - 1), \]`

where:

- ( M ) is the monthly payment,

- ( P ) is the principal amount (amount financed),

- ( r ) is the monthly interest rate (annual interest rate divided by 12 and converted to a decimal),

- ( n ) is the total number of payments (loan term in months).

In this case:

- ( P = 14,900 - 2,300 = 12,600 ) (amount financed),

-
`\( r = (7.5\%)/(12 * 100) = 0.00625 \)` (monthly interest rate),

- ( n = 48 ) (loan term in months).

Now, substitute these values into the formula:

`\[ M = (12,600 \cdot 0.00625 \cdot (1 + 0.00625)^(48))/((1 + 0.00625)^(48) - 1). \]`

Calculating this expression gives the monthly payment, which turns out to be approximately $310.51.

Therefore, Cody Lind's monthly car payment, based on a 48-month, 7.5% loan, is approximately $310.51.