Final answer:
To determine the monthly payment for borrowing $12,000 at 6% for five years towards a car purchase, use the annuity payment formula. For Installment Loan A of $14,000 at 5.1% over three years, apply the same formula with adjusted values to find the monthly payment and total interest.
Step-by-step explanation:
To calculate the monthly payment for borrowing $12,000 at 6% for five years for a car purchase, we can use the formula for the annuity payment in finance, which is often presented as:
PMT = P × rac{i(1 + i)^n}{(1 + i)^n - 1}
where PMT represents the monthly payment, P is the principal amount of $12,000, i is the monthly interest rate (which is 6% per year or 0.06/12 per month), and n is the total number of payments (which is 5 years × 12 months/year = 60 payments).
Plugging in these values:
PMT = $12,000 × rac{(0.06/12)(1 + 0.06/12)^60}{(1 + 0.06/12)^60 - 1}
After solving the formula, we will find the monthly payment.
For the second part of your question regarding Installment Loan A, which is a three-year loan at 5.1%, we use a similar approach. The principal now is $14,000, and the monthly interest rate is 5.1% per year or 0.051/12 per month. The total number of payments is 3 years × 12 months/year = 36 payments.
The formula will now be:
PMT = $14,000 × rac{(0.051/12)(1 + 0.051/12)^36}{(1 + 0.051/12)^36 - 1}
Once the monthly payment is calculated, the total interest paid over the life of loan A can be found by multiplying the monthly payment by the number of payments (36) and subtracting the principal amount ($14,000).