Final answer:
To find the largest loan you can apply for with a $3,500 down payment, consider that this is 10% of the total car price, indicating a car price of $35,000 and a loan amount of $31,500. The remaining principal after three years would depend on the loan's terms and payment schedule. Simple interest examples include a $5,000 loan at 6% over three years yielding $900 in interest and a $10,000 loan at 1% over five years yielding $500 in interest.
Step-by-step explanation:
The question posed is related to calculating the largest loan one can take out with a given down payment and determining the remaining principal after a certain period on an auto loan.
Loan Calculation
If you have $3,500 saved for a down payment and the bank requires a 10% down payment, the largest loan you can apply for would be 90% of the total car value. Mathematically speaking, if 10% is $3,500, the car's full value is $3,500 / 0.10 which is $35,000. Thus, the maximum loan amount would be $35,000 - $3,500 which is $31,500.
Calculating Remaining Principal
The question about how much principal will remain after three years requires additional information. We would need the initial loan terms and an amortization schedule to calculate the exact remaining principal. However, generally, with each monthly payment, a portion goes towards the principal and another towards the interest, gradually reducing the principal over time.
Sample Interest Calculations
To answer the sample questions provided:
- The total interest from a $5,000 loan after three years at a simple interest rate of 6% equals $900 (Interest = Principal x Rate x Time).
- If you receive $500 in simple interest from a $10,000 loan over five years, the interest rate charged is 1% per year (Interest = Principal x Rate x Time).