the williams are buying a house that costs $323,000 and can afford a 10% down payment. if the williams want…
the williams are buying a house that costs $323,000 and can afford a 10% down payment. if the williams want the lowest monthly payment, which loan option would you recommend?\na. 15 year fixed, 5% down at a fixed rate of 5.5%\nb. 30 year fha, 3.5% down at a fixed rate of 6.25%\nc. 30 year fixed, 20% down at a fixed rate of 5.75%\nd. 30 year fixed, 10% down at a fixed rate of 6%\nplease select the best answer from the choices provided
Answer
Explanation:
Step1: Calculate loan - amount for each option
The house costs $323,000. For option a: Down - payment = 0.05×323000 = 16150, Loan amount = 323000−16150 = 306850. For option b: Down - payment = 0.035×323000 = 11305, Loan amount = 323000−11305 = 311695. For option c: Down - payment = 0.2×323000 = 64600, Loan amount = 323000−64600 = 258400. For option d: Down - payment = 0.1×323000 = 32300, Loan amount = 323000−32300 = 290700.
Step2: Use the mortgage payment formula $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $M$ is the monthly payment, $P$ is the loan amount, $r$ is the monthly interest rate, and $n$ is the total number of payments.
For a 15 - year loan (option a), $n = 15×12=180$ months and $r=\frac{0.055}{12}$. For a 30 - year loan (options b, c, d), $n = 30×12 = 360$ months. For option b, $r=\frac{0.0625}{12}$; for option c, $r=\frac{0.0575}{12}$; for option d, $r=\frac{0.06}{12}$. Option c has the largest down - payment (20%), resulting in the smallest loan amount among the 30 - year options, and a relatively low interest rate.
Answer:
C