Use the Zillow Mortgage Calculator to determine the monthly loan payment for a $345,000 loan at 4.2% for 30 years. Do not include any taxes, insurance, fees or other costs. Round your answer to the NEAREST WHOLE DOLLAR, but do not include a $ sign with your response.
Answer (2)
The monthly loan payment for a $345,000 loan at an interest rate of 4.2% for 30 years is approximately 1633 when rounded to the nearest whole dollar. This was calculated using the loan payment formula and careful substitution of values. The monthly interest rate and total number of payments were also determined as part of the calculation.
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Calculate the monthly interest rate: i = 12 0.042 = 0.0035 .
Calculate the total number of payments: n = 30 × 12 = 360 .
Use the loan payment formula: M = P ( 1 + i ) n − 1 i ( 1 + i ) n = 345000 × ( 1 + 0.0035 ) 360 − 1 0.0035 ( 1 + 0.0035 ) 360 .
Calculate the monthly payment and round to the nearest dollar: M = 1687 .
Explanation
Understanding the Problem We are asked to calculate the monthly loan payment for a loan of $345,000 at an annual interest rate of 4.2% for a term of 30 years. We need to round the final answer to the nearest whole dollar. The formula for calculating the monthly payment (M) is:
M = P ( 1 + i ) n − 1 i ( 1 + i ) n
where:
P is the principal loan amount
i is the monthly interest rate
n is the total number of payments
Calculating the Values First, we need to determine the values for P, i, and n.
P (principal loan amount) = $345,000
i (monthly interest rate) = annual interest rate / 12 = 0.042 / 12 = 0.0035
n (total number of payments) = loan term in years * 12 = 30 * 12 = 360
Substituting the Values Now, we substitute these values into the formula:
M = 345000 × ( 1 + 0.0035 ) 360 − 1 0.0035 ( 1 + 0.0035 ) 360
Calculating this expression, we get:
M = 345000 × ( 1.0035 ) 360 − 1 0.0035 ( 1.0035 ) 360
M = 345000 × 3.8475 − 1 0.0035 × 3.8475
M = 345000 × 2.8475 0.013466
M = 345000 × 0.00473
Calculating the Monthly Payment After performing the calculation, we find that:
M = 1632.15
Rounding this to the nearest whole dollar, we get $1632.
Final Answer Therefore, the monthly loan payment, rounded to the nearest whole dollar, is 1687.
Examples
Understanding loan payments is crucial in personal finance. For instance, when buying a house, knowing the monthly mortgage payment helps in budgeting and financial planning. The loan payment formula is also applicable in other scenarios, such as calculating car loan payments or understanding the impact of different interest rates and loan terms on the total amount paid over time. By mastering these calculations, individuals can make informed decisions about borrowing and managing their finances effectively.
