Final answer:
To calculate the loan payment, convert the APR to a monthly rate, divide it by 12, and apply it to the term of the loan in months using the annuity formula. An example is given for how to solve using the formula, as well as applying it to a specific scenario involving a known annual budget for housing loan payments.
Step-by-step explanation:
The question pertains to calculating loan payments with a given annual percentage rate (APR) and term. While the exact loan amount is not provided, we can infer the process to calculate the monthly payment. Using a standard loan payment formula, which is the annuity formula: P = [rPV] / [1 - (1 + r)^{-n}], where P is the payment, r is the monthly interest rate, PV is the present value, or principal amount, and n is the number of payments.
When calculating the loan payment, you would need to convert the APR to a monthly rate by dividing by 12, and then apply it within the context of the given term of the loan expressed in months. As an example, for a $100,000 loan at an APR of 10% over a 5-year term, the monthly rate (r) would be 0.10/12 and the number of monthly payments (n) would be 5*12. With these values, you can solve for the monthly payment (P) using the formula.
For a more specific application, in the case of Joanna knowing she can afford $12,000 per year on a house loan with a 4.2% annual interest rate over 30 years, we could use the formula to determine the maximum loan she can afford and the total amount she would pay after 30 years. The method to determine Joanna's scenario involves first calculating the monthly payment since $12,000 per year translates to $1,000 per month and then using the present value formula that considers the annual interest rate and loan term.