Question

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 A B C D.

Answer 1

Since the Johnsons want the lowest monthly payment, the recommended loan option is Option B.

Data and Calculations:

a. 30 year FHA, 3.5% down at a fixed rate of 6.25%

Monthly Pay:   $1,247.75

House Price $210,000.00

Loan Amount = $202,650.00 ($210,000 - $7,350)

Down Payment = $7,350.00 ($210,000 x 3.5%)

Total of 360 Mortgage Payments = $449,190.33

Total Interest = $246,540.33

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

Monthly Pay:   $1,007.24

House Price $210,000.00

Loan Amount $168,000.00 ($210,000 - $42,000)

Down Payment = $42,000.00 ($210,000 x 20%)

Total of 360 Mortgage Payments = $362,608.16

Total Interest = $194,608.16

c. 30 year fixed, 10% down at a fixed rate of 6%

Monthly Pay:   $1,133.15

House Price $210,000.00

Loan Amount $189,000.00 ($210,000 - $21,000)

Down Payment = $21,000.00 ($210,000 x 10%)

Total of 360 Mortgage Payments = $407,934.18

Total Interest = $218,934.18

d. 15 year fixed, 20% down at a fixed rate 5.5%

Monthly Pay:   $1,372.70

House Price $210,000.00

Loan Amount $168,000.00 ($210,000 - $42,000)

Down Payment = $42,000.00 ($210,000 x 20%)

Total of 180 Mortgage Payments = $247,086.04

Total Interest = $79,086.04

Thus, the lowest monthly payment goes with Option B.

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Answer 2

The correct statement is that Johnson should choose for the loan of 30 years at 20% down payment at the rate of interest at 6%. So, the correct option is B.

The computation of the cheapest monthly payments can be done by the comparison of all the loan options available by calculation of monthly payments in each scenario.

Calculation of Monthly Payments

• The formula for the calculation of the monthly payments is as below,

• $\rm Monthly\ Payments = \dfrac {Annuity}{No.\ of\ Months }$

• The calculation of annuity can be done using the below formula given that 20% of the amount is paid as down payment upfront which is computed as $42,000 so, principal loan amount is $168,000.

• $\rm Annuity\ for\ loan\ B= 168000(1+\dfrac{0.06}{1})^1^x\ ^3^0\\\\\rm Annuity\ for\ loan\ B= \ 362,608.16$

• Now the monthly payments can be calculated by using the formula given above as,

• $\rm Monthly\ Payment\ for\ Loan\ B = \dfrac{\ 362,608.16}{360}\\\\\rm Monthly\ Payment\ for\ Loan\ B = \ 1007.42$

• Monthly payment for Loan B is calculated as $1007.42 whereas the monthly payments for Loans A, C and D are calculated as $1,247.75, $1,133.15 and $1,372.70 respectively.

• So, it can be concluded that the cheapest option of loan for monthly payments is 20% down payment with 30 years loan at a rate of 6%.

Hence, the correct option is B that the loan with characteristics as in Loan B is the most suitable and cheapest loan option for Johnson's house loan with respect to monthly payments.

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