Questions: Select the formula you need to use to solve this problem: Katie is purchasing her first home for 129,000. She makes a downpayment of 10% and mortgages the rest at 3.15% interest for 15 years. What is her monthly payment amount? Simple interest, A=P(1+rt) Loans formula Payout annuity formula Annuity formula Compound interest Simple interest, I= Prt

Solution Steps

To determine Katie's monthly mortgage payment, we need to use the loan formula for calculating monthly payments on a fixed-rate mortgage. The formula is derived from the annuity formula, which calculates the periodic payment required to pay off a loan over a specified term at a fixed interest rate. First, calculate the loan amount by subtracting the down payment from the purchase price. Then, apply the loan formula to find the monthly payment.

The down payment is calculated as follows: \[ \text{Down Payment} = \frac{10}{100} \times 129000 = 12900 \]

The loan amount is determined by subtracting the down payment from the purchase price: \[ \text{Loan Amount} = 129000 - 12900 = 116100 \]

The annual interest rate is converted to a monthly rate, and the loan term is converted to months: \[ \text{Interest Rate (Monthly)} = \frac{3.15}{100} \div 12 = 0.002625 \] \[ \text{Loan Term (Months)} = 15 \times 12 = 180 \]

Using the loan formula, the monthly payment is calculated as follows: \[ \text{Monthly Payment} = \frac{116100 \times 0.002625}{1 - (1 + 0.002625)^{-180}} \approx 810.1675 \]

Final Answer