Final answer:
To calculate how much the couple can spend on a home with their budget and down payment at a 6.1% interest rate, we must first find the present value of their monthly loan payments over 25 years, and then add the down payment amount to this figure.
Step-by-step explanation:
The couple is considering a 25-year loan and has a budget of $1,200 per month for their loan payment, with $29,000 available for a down payment. To determine how much they can spend on a home at a 6.1% interest rate, we can use the present value of an annuity formula. However, you didn't provide the complete interest rate options (like 6.1% annually, monthly, etc.), so I will assume it is an annual rate to perform the calculation.
First, we need to calculate the present value of the payments they can afford, which is essentially the maximum loan amount they can take out. The monthly loan payment is $1,200, and for a 25-year loan at an annual interest rate of 6.1%, we convert this rate to a monthly rate by dividing it by 12. Therefore, we have:
- Monthly interest rate = 6.1% / 12
- Number of payments = 25 years * 12 months
By applying these values to a financial calculator or a relevant formula, we can find the present value, which is the amount they can borrow under these terms. Once we have this, we add it to the $29,000 down payment to find the total price of the home they can afford.