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You want to buy a new car. With payments of $300 per month and a 5.1% annual interest rate compounded monthly for 5 years, how much can you borrow?

a. $15,000
b. $16,200
c. $17,500
d. $18,800

User Hevi
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1 Answer

3 votes

Final answer:

To calculate the amount that can be borrowed, use the formula for the present value of an annuity: Present Value = Payment * (1 - (1+r)^(-n)) / r. Plugging in the given values, the amount that can be borrowed is approximately $16,180.92.

Step-by-step explanation:

To calculate the amount that can be borrowed, we can use the formula for the present value of an annuity:

Present Value = Payment * (1 - (1+r)^(-n)) / r

Where Payment is the monthly payment, r is the monthly interest rate, and n is the number of payments.

In this case, the payment is $300, the annual interest rate is 5.1%, and the loan term is 5 years (60 monthly payments).

First, we need to convert the annual interest rate to a monthly rate by dividing it by 12 (12 months in a year). So the monthly interest rate is 5.1%/12 = 0.425% or 0.00425.

Using the formula, we can calculate the present value:

Present Value = $300 * (1 - (1+0.00425)^(-60)) / 0.00425

Calculating this expression, we find that the present value is approximately $16,180.92.

Therefore, you can borrow approximately $16,180.92 (option b).

User Ruba
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