Final answer:
To calculate the monthly payment on a $20,000 loan with a 5-year term and a 6% interest rate, use the loan's principal, the monthly interest rate, and the number of monthly installments in the loan payment formula. Find the monthly rate by dividing the annual rate by 12, convert the percentage to a decimal, determine the total number of monthly payments, and substitute the values into the formula and solve.
Step-by-step explanation:
Calculating the Monthly Mortgage Payment
To calculate the monthly payment for a $20,000 loan with a 5-year term and an annual interest rate of 6%, you would use the formula for the monthly payment on an installment loan which considers the principal amount, the interest rate, and the number of payments.
The formula to use is:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]
Where:
- M is the monthly payment
- P is the principal loan amount ($20,000)
- i is the monthly interest rate (annual rate/12)
- n is the number of payments (term of the loan in months)
Step 1: Convert the annual interest rate to a monthly rate by dividing by 12:
i = 6% / 12 = 0.5%
Step 2: Convert the percentage to a decimal for calculation:
i = 0.5% = 0.005
Step 3: Multiply the term in years by 12 to find the number of monthly payments:
n = 5 years × 12 months/year = 60 months
Step 4: Plug the values into the formula to solve for M:
M = $20,000 [ 0.005(1 + 0.005)^60 ] / [ (1 + 0.005)^60 – 1 ]
Carefully calculate the values within the brackets and then solve for M to determine the monthly payment. Note that it's important to follow the correct order of operations while performing the calculation.