question asked :
You need $12,000 to buy a car.
You will pay uncle back in 5 years, with one payment each year.
The interest rate is 8%.
Question A: How much will you pay each year?
Question B: How much of your first payment will go to interest and how much will go to principal?
annual_payment = (principal * (1 + interest)^number_of_payments) / ((1 + interest)^number_of_payments - 1)
principal is $12,000, the interest rate is 8% & number of payments is 5
Sure, I can help you with that.
**a. What will be your annual loan payments?**
The formula for calculating the annual loan payments for an amortized loan is:
annual_payment = (principal * (1 + interest)^number_of_payments) / ((1 + interest)^number_of_payments - 1)
In this case, the principal is $12,000, the interest rate is 8%, and the number of payments is 5. So, the annual loan payments are:
```
annual_payment = (12000 * (1 + 0.08)^5) / ((1 + 0.08)^5 - 1) = 1633.39
```
Therefore, your annual loan payments will be **$1,633.39**.
**b. How much of your first payment will be applied to interest and to principal repayment?**
The first payment will be applied to both interest and principal repayment. The amount of interest that will be paid in the first payment is:
```
interest = annual_payment * interest_rate = 1633.39 * 0.08 = 130.67
```
The amount of principal repayment in the first payment is:
```
principal_repayment = annual_payment - interest = 1633.39 - 130.67 = 1502.72
```
Therefore, **$130.67** of your first payment will be applied to interest and **$1,502.72** will be applied to principal repayment.