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This morning, you borrowed $162,000 to buy a house. The mortgage rate is 4.35 percent. The loan is to be repaid in equal monthly payments over 20 years with the first payment due one month from today. Assume each month is equal to 1/12 of a year and all taxes and insurance premiums are paid separately. How much of the second payment applies to the principal balance?

Respuesta :

lestat345

Answer:

[tex]\$ 433.35[/tex] of the second payment applies to the principal balance

Step-by-step explanation:

Hi

Known data

  • [tex]P=162000[/tex]
  • [tex]i_{Y}=4.35\%=0.0435[/tex]
  • [tex]n=20 years=240 months[/tex]

The first step is to find the monthly interest, so we use [tex]1+i_{Y}=(1+i_{M})^{12}[/tex] to do it. Then we have, [tex]1+0.0435=(1+i_{M})^{12}[/tex],

[tex]i_{M}=\sqrt[12]{1.0435}-1=1.0035-1=0.0035[/tex]

the second step is to find the value of the equal monthly payments with the formula below.

[tex]K=\frac{P}{\frac{1-(1+i_{M})^{-n}}{i_{M}} } =\frac{162000}{\frac{1-(1+0.0035)^{-240}}{0.0035} }=998.84[/tex]

Third, we need to calculate the capital subscription in the two first periods

[tex]I_{1}=P*i_{M}=162000(0.0035)=567\\CS_{1}=K-I_{1}=998.84-567=431.84\\B_{1}=P-CS_{1}=162000-431.84=161568.15[/tex]

[tex]I_{2}=B_{1}*i_{M}=161568.15(0.0035)=565.48\\CS_{2}=K-I_{2}=998.84-565.48=433.35\\\left[CS_{2}=433.35\right][/tex]