Question

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You can afford a $450 per month car payment. You've found a 3 year loan at 4.8% annual interest rate, compounded monthly. How big of a loan amount can you afford? (Enter numeric answers to 2 decimal places.)

Answer 1

Answer:

Monthly payment (

�

M) = $450

Annual interest rate (

�

r) = 4.8% or 0.048 (expressed as a decimal)

Loan term in years (

�

n) = 3 years

Let's solve for

�

P:

450

=

�

×

0.004

1

−

(

1

+

0.004

)

−

36

450=P×

1−(1+0.004)

−36

0.004

​

Now, calculate the loan amount

�

P:

�

=

450

×

(

1

−

(

1

+

0.004

)

−

36

)

0.004

P=

0.004

450×(1−(1+0.004)

−36

)

​

Let's compute this value:

�

≈

450

×

(

1

−

0.820758

)

0.004

≈

450

×

0.179242

0.004

≈

80.659

0.004

≈

20164.75

P≈

0.004

450×(1−0.820758)

​

≈

0.004

450×0.179242

​

≈

0.004

80.659

​

≈20164.75

So, you can afford a loan amount of approximately $20,164.75.

Step-by-step explanation: