Final answer:
To calculate the monthly payment for a $50,000 student loan at a 6% APR for 20 years, use the loan payment formula. The monthly payment is approximately $358.22.
Step-by-step explanation:
Calculating the Monthly Payment on a Student Loan
To calculate the monthly payment of a $50,000 student loan with a fixed APR of 6% for 20 years, we can use the formula for a fixed installment loan. The formula incorporates the loan amount (principal), the interest rate per period, and the total number of payments or periods. Since the interest rate given is annual, we need to convert it to a monthly rate by dividing by 12. The formula we will use is:
A = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
- A is the monthly payment,
- P is the loan principal ($50,000),
- r is the monthly interest rate (6% annual divided by 12 months),
- n is the number of payments (20 years times 12 months).
First, convert the annual interest rate to a monthly rate by dividing 6% (or 0.06) by 12, which gives 0.005. Then, multiply the number of years (20) by 12 to get the total number of monthly payments, which is 240. Substituting the values into the loan formula gives us the monthly payment A:
A = $50,000 * (0.005(1+0.005)^240) / ((1+0.005)^240 - 1) = $358.22 approximately.
Therefore, the monthly payment for a $50,000 student loan at 6% APR for 20 years is about $358.22.