the johnsons are buying a house that costs $210,000 and can afford a 20% down payment. if the johnsons want…

the johnsons are buying a house that costs $210,000 and can afford a 20% down payment. if the johnsons want the lowest monthly payment, which loan option would you recommend? a. 30 year fha, 3.5% down at a fixed rate of 6.25% b. 30 year fixed, 20% down at a fixed rate of 6% c. 30 year fixed, 10% down at a fixed rate of 6% d. 15 year fixed, 20% down at a fixed rate 5.5% please select the best answer from the choices provided

the johnsons are buying a house that costs $210,000 and can afford a 20% down payment. if the johnsons want the lowest monthly payment, which loan option would you recommend? a. 30 year fha, 3.5% down at a fixed rate of 6.25% b. 30 year fixed, 20% down at a fixed rate of 6% c. 30 year fixed, 10% down at a fixed rate of 6% d. 15 year fixed, 20% down at a fixed rate 5.5% please select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate loan - amount for each option

The house costs $210,000. For option a: Down - payment is $0.035\times210000 = 7350$, loan amount $L_a=210000 - 7350=202650$. For option b: Down - payment is $0.2\times210000 = 42000$, loan amount $L_b=210000 - 42000 = 168000$. For option c: Down - payment is $0.1\times210000 = 21000$, loan amount $L_c=210000 - 21000 = 189000$. For option d: Down - payment is $0.2\times210000 = 42000$, loan amount $L_d=210000 - 42000 = 168000$.

Step2: Recall the monthly - payment formula

The monthly - payment formula for a fixed - rate loan is $M = P\frac{r(1 + r)^n}{(1 + r)^n-1}$, where $P$ is the loan amount, $r$ is the monthly interest rate, and $n$ is the total number of payments. For a 30 - year loan, $n = 30\times12=360$ months. For a 15 - year loan, $n = 15\times12 = 180$ months. For option a: $r_a=\frac{0.0625}{12}$, $P = L_a = 202650$, $n = 360$. For option b: $r_b=\frac{0.06}{12}$, $P = L_b = 168000$, $n = 360$. For option c: $r_c=\frac{0.06}{12}$, $P = L_c = 189000$, $n = 360$. For option d: $r_d=\frac{0.055}{12}$, $P = L_d = 168000$, $n = 180$.

Step3: Analyze the impact of loan amount, interest rate, and loan term on monthly payment

The monthly payment is directly related to the loan amount and the interest rate, and inversely related to the loan term (for a fixed loan amount and interest rate, a shorter - term loan has a higher monthly payment). Option a has a higher loan amount compared to options b and d (after down - payment) and a relatively high interest rate. Option c has a higher loan amount than option b. Option d has a shorter loan term compared to options a, b, and c, so it will have a higher monthly payment despite the lower interest rate and same down - payment as option b. Option b has a 20% down - payment (which the Johnsons can afford) and a relatively low interest rate among the 30 - year options.

Answer:

B. 30 year fixed, 20% down at a fixed rate of 6%