Final answer:
Sean can pay around $3807.45 for a car, given his monthly payments of $120 for 3 years, at an interest rate of 9% compounded monthly.
Step-by-step explanation:
The subject of this problem is a financial math question. It involves calculating the total loan Sean can take out if he can make $120 payments per month, for 3 years, at an interest rate of 9% compounded monthly. We can use the formula for the present value of an ordinary annuity to calculate this, which is: P = PMT * [(1 - (1 + r)^-n) / r], where:
- P is the total loan (the principal)
- PMT is the monthly payment
- r is the monthly interest rate
- n is the number of payments
Converting the annual interest rate into a monthly rate, we get r = 9 / 12 / 100 = 0.0075. Sean will make payments for 3 years, which equals 3*12=36 months. Plugging these values into the formula we get P = $120 * [(1 - (1 + 0.0075) ^ -36) / 0.0075] which equals approximately $3807.45, which is the amount Sean can pay for a car with the given loan conditions.
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