Respuesta :
Case 11: Amount of monthly payment is $551.25
Case 12: Amount of monthly payment is $1361.77
Case 13: Amount of monthly payment is $814.03
Case 14: Amount of monthly payment is $656.25
Case 15: Amount of monthly payment is $897.6
Case 16: Amount of monthly payment is $2018.26
Step-by-step explanation:
Case 11:
Step 1: converting your annual interest rate to a monthly interest rate by dividing by 12
Monthly rate = [tex]\frac{8 \%}{12}=\frac{0.08}{12}=0.00666[/tex]
Step 2: add 1 to the monthly rate
1+0.00666 = 1.00666
Step 3: multiply the number of years in the term of the mortgage by 12 to calculate the number of monthly payments you’ll make
The number of monthly payments = 30(12) = 360 months
Step 4: raise the result of 1 plus the monthly rate to the negative power of the number of monthly payments
[tex]1.00666^{(-360)}[/tex] = 0.0936
Step 5: subtract that result (obtained from step 4) from 1
1 – 0.0936 = 0.906
Step 6: divide the monthly rate by the result obtained from step 5
[tex]\frac{0.0066}{0.906}=0.00735[/tex]
Step 7: multiple the result by the amount you borrowed ($75,000).
Amount of monthly payment= 0.00735(75000) = $551.25
Case 12:
Step 1: converting your annual interest rate to a monthly interest rate by dividing by 12
Monthly rate = [tex]\frac{11 \%}{12}=\frac{0.11}{12}=0.00916[/tex]
Step 2: add 1 to the monthly rate
1+0.00916 = 1.00916
Step 3: multiply the number of years in the term of the mortgage by 12 to calculate the number of monthly payments you’ll make
The number of monthly payments = 20(12) = 240 months
Step 4: raise the result of 1 plus the monthly rate to the negative power of the number of monthly payments
[tex]1.00916^{(-240)}=0.1121[/tex]
Step 5: subtract that result (obtained from step 4) from 1
1 – 0.1121 = 0.8879
Step 6: divide the monthly rate by the result obtained from step 5
[tex]\frac{0.00916}{0.8879}=0.0103[/tex]
Step 7: multiple the result by the amount you borrowed ($132,000).
Amount of monthly payment= 0.0103(132000) = $1361.77
Similarly,
Case 13:
Monthly rate = [tex]\frac{9 \%}{12}=\frac{0.09}{12}=0.0075[/tex]
1+0.0075 = 1.0075
The number of monthly payments = 25(12) = 300 months
[tex]1.0075^{(-300)}=0.1063[/tex]
1 – 0.1063 = 0.8937
[tex]\frac{0.0075}{0.8937}=0.0084[/tex]
Amount of monthly payment= 0.0084(97000) = $814.03
Case 14:
Monthly rate = [tex]\frac{8 \%}{12}=\frac{0.08}{12}=0.00666[/tex]
1+0.00666 = 1.00666
The number of monthly payments = 30(12) = 360 months
[tex]1.00666^{(-360)}=0.09166[/tex]
1 – 0.09166 = 0.9083
[tex]\frac{0.00666}{0.9083}=0.0073[/tex]
Amount of monthly payment= 0.0073(89500) = $656.25
Case 15:
Monthly rate = [tex]\frac{10 \%}{12}=\frac{0.10}{12}=0.00833[/tex]
1+0.00833 = 1.00833
The number of monthly payments = 10(12) = 120 months
[tex]1.00833^{(-120)}=0.36955[/tex]
1 – 0.36955 = 0.6304
[tex]\frac{0.00833}{0.6304}=0.0132[/tex]
Amount of monthly payment= 0.0132(68,000) = $897.6
Case 16:
Monthly rate = [tex]\frac{9 \%}{12}=\frac{0.09}{12}=0.0075[/tex]
1+0.0075 = 1.0075
The number of monthly payments = 15(12) = 180 months
[tex]1.0075^{(-180)}=0.2605[/tex]
1 – 0.2605 = 0.7395
[tex]\frac{0.0075}{0.7395}=0.01014[/tex]
Amount of monthly payment= 0.01014(199,000) = $2018.26
