Elena is looking to buy a car for $10,000. She is planning to buy this car by borrowing 60% of the car price. The bank is happy to do the loan for 3 years at a rate of 7.67% per year. Calculate the monthly car loan repayment

In your answer, ignore the "$" and enter with 2 decimal places

Question

Elena is looking to buy a car for $10,000. She is planning to buy this car by borrowing 60% of the car price. The bank is happy to do the loan for 3 years at a rate of 7.67% per year. Calculate the monthly car loan repayment

In your answer, ignore the "$" and enter with 2 decimal places

BlackTom AI · Accepted Answer

First, identify the loan details from the problem. The car price is 10,000, and Elena plans to borrow 60% of this amount, so the loan principal P = 0.60 × 10,000 = 6,000. The annual interest rate is 7.67%, and the loan term is 3 years, which means the number of monthly payments n = 3 × 12 = 36. The monthly interest rate is i = 7.67% ÷ 12 = 0.0767 ÷ 12 ≈ 0.0063916667 per month.

Next, apply the standard fixed-rate loan payment formula, which gives the monthly payment M as:
M = P × i / [1 − (1 + i)^(−n)].

Plug in the numbers: M = 6,000 × 0.0063916667 / [1 − (1 + 0.0063916667)^(−36)].
Compute the denominator term step by step: first compute (1 + i) = 1.0063916667, then raise it to the power of −36 to get (1.0063916667)^(−36). Depending on rounding, this value is approximately around 0.8 (since (1 + i)^36 is a bit over 1.25 for this interest rate, the inverse is a bit under 0.8). Therefore, 1 − (1 + i)^(−36) is roughly 0.20+. Using a more precise calculation yields a denominator near 0.2041.

Then the numerator P × i = 6,000 × 0.0063916667 ≈ 38.3500002. Dividing by the computed denominator around 0.2041 gives a monthly payment M ≈ 38.35 / 0.2041 ≈ 187.1. When rounded to two decimal places, the monthly repayment is approximately 187.11.

Summary of the steps:
- Compute principal: P = 6,000
- Compute monthly rate: i ≈ 0.0063916667
- Compute number of payments: n = 36
- Use M = P × i / [1 − (1 + i)^(−n)]
- Evaluate to two decimals: M ≈ 187.11

Elena is looking to buy a car for $10,000. She is planning to buy this car by borrowing 60% of the car price. The bank is happy to do the loan for 3 years at a rate of 7.67% per year. Calculate the monthly car loan repayment In your answer, ignore the "$" and enter with 2 decimal places简答题

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