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11 months ago

you wish to buy a $25,000 car. the dealer offers you a 4-year loan with a 9 percent apr. what are the monthly payments?

Business

1 answer:

NeTakaya11 months ago

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In order to buy a car worth $25,000 a monthly payment of $622.12 is required.

Mortgages are one type of loan that frequently has a structure that calls for a stream of identical monthly payments. The lender can assess whether the customer's budget can support equal monthly payments by doing so.

Suppose the monthly payment is M.

With 9 percent APR, the effective monthly rate is 9%/12 = 0.75%.

There will be 12 x 4 years, or 48 monthly payments.

The face value of the loan must be equal to the present value of these monthly payments, or

${}\sum_{t=1}^{48}{\frac{M}{(1 + 0.75\%)^t}} = 25,000, {}$

which yields M = 622.12.

If you only paid interest, the monthly payment would be calculated as follows: principal * monthly interest rate (9% /12) = 25,000*0.75% = 187.5.

The results would be that after five years, you would still owe the whole amount of $25,000 and would have to pay $11,250 in interest.

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