Solved on Feb 05, 2024

Diane bought $\$ 12,600$ in lab equipment, paying $\$ 1200$ down and taking out a loan for the rest. She paid $\$ 505.26$ monthly for 2 years to pay off the loan. (a) What was the total cost? (b) How much interest did she pay?

STEP 1

Assumptions
1. The total cost of the lab equipment is $12,600.<br />2. Diane made a down payment of$ 1,200.
3. The remaining amount was taken as a business loan.
4. Diane paid off the loan with monthly payments of $505.26 over 2 years.
5. The total amount paid includes the down payment and the monthly payments.

STEP 2

Calculate the amount Diane took out as a loan by subtracting the down payment from the total cost of the equipment.
$Loan\, amount = Total\, cost - Down\, payment$

STEP 3

Plug in the given values to calculate the loan amount.
$Loan\, amount = \$12,600 - \$1,200$

STEP 4

Calculate the loan amount.
$Loan\, amount = \$12,600 - \$1,200 = \$11,400$

STEP 5

Calculate the total number of monthly payments Diane made over the 2 years.
$Total\, monthly\, payments = Number\, of\, years \times 12\, months\, per\, year$

STEP 6

Plug in the values for the number of years to calculate the total number of monthly payments.
$Total\, monthly\, payments = 2 \times 12$

STEP 7

Calculate the total number of monthly payments.
$Total\, monthly\, payments = 2 \times 12 = 24$

STEP 8

Calculate the total amount paid through monthly payments by multiplying the monthly payment amount by the total number of monthly payments.
$Total\, paid\, through\, monthly\, payments = Monthly\, payment \times Total\, monthly\, payments$

STEP 9

Plug in the values for the monthly payment amount and the total number of monthly payments to calculate the total paid through monthly payments.
$Total\, paid\, through\, monthly\, payments = \$505.26 \times 24$

STEP 10

Calculate the total paid through monthly payments.
$Total\, paid\, through\, monthly\, payments = \$505.26 \times 24 = \$12,126.24$

STEP 11

Calculate the total amount Diane ended up paying for the equipment by adding the down payment to the total paid through monthly payments.
$Total\, amount\, paid = Down\, payment + Total\, paid\, through\, monthly\, payments$

STEP 12

Plug in the values for the down payment and the total paid through monthly payments to calculate the total amount paid.
$Total\, amount\, paid = \$1,200 + \$12,126.24$

STEP 13

Calculate the total amount Diane ended up paying for the equipment.
$Total\, amount\, paid = \$1,200 + \$12,126.24 = \$13,326.24$
Diane ended up paying $13,326.24 for the equipment.
(a) The total amount Diane ended up paying for the equipment (including the down payment and monthly payments) is $\$ 13,326.24$ .

STEP 14

To find out how much interest Diane paid on the loan, subtract the original loan amount from the total amount paid through monthly payments.
$Interest\, paid = Total\, paid\, through\, monthly\, payments - Loan\, amount$

STEP 15

Plug in the values for the total paid through monthly payments and the loan amount to calculate the interest paid.
$Interest\, paid = \$12,126.24 - \$11,400$

STEP 16

Calculate the amount of interest Diane paid on the loan.
$Interest\, paid = \$12,126.24 - \$11,400 = \$726.24$
(b) The amount of interest Diane paid on the loan is $\$ 726.24$ .

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Diane bought $\$ 12,600$ in lab equipment, paying $\$ 1200$ down and taking out a loan for the rest. She paid $\$ 505.26$ monthly for 2 years to pay off the loan. (a) What was the total cost? (b) How much interest did she pay?

STEP 1

STEP 2

Calculate the amount Diane took out as a loan by subtracting the down payment from the total cost of the equipment.
$Loan\, amount = Total\, cost - Down\, payment$

STEP 3

Plug in the given values to calculate the loan amount.
$Loan\, amount = \$12,600 - \$1,200$

STEP 4

Calculate the loan amount.
$Loan\, amount = \$12,600 - \$1,200 = \$11,400$

STEP 5

Calculate the total number of monthly payments Diane made over the 2 years.
$Total\, monthly\, payments = Number\, of\, years \times 12\, months\, per\, year$

STEP 6

Plug in the values for the number of years to calculate the total number of monthly payments.
$Total\, monthly\, payments = 2 \times 12$

STEP 7

Calculate the total number of monthly payments.
$Total\, monthly\, payments = 2 \times 12 = 24$

STEP 8

Calculate the total amount paid through monthly payments by multiplying the monthly payment amount by the total number of monthly payments.
$Total\, paid\, through\, monthly\, payments = Monthly\, payment \times Total\, monthly\, payments$

STEP 9

Plug in the values for the monthly payment amount and the total number of monthly payments to calculate the total paid through monthly payments.
$Total\, paid\, through\, monthly\, payments = \$505.26 \times 24$

STEP 10

Calculate the total paid through monthly payments.
$Total\, paid\, through\, monthly\, payments = \$505.26 \times 24 = \$12,126.24$

STEP 11

Calculate the total amount Diane ended up paying for the equipment by adding the down payment to the total paid through monthly payments.
$Total\, amount\, paid = Down\, payment + Total\, paid\, through\, monthly\, payments$

STEP 12

Plug in the values for the down payment and the total paid through monthly payments to calculate the total amount paid.
$Total\, amount\, paid = \$1,200 + \$12,126.24$

STEP 13

STEP 14

To find out how much interest Diane paid on the loan, subtract the original loan amount from the total amount paid through monthly payments.
$Interest\, paid = Total\, paid\, through\, monthly\, payments - Loan\, amount$

STEP 15

Plug in the values for the total paid through monthly payments and the loan amount to calculate the interest paid.
$Interest\, paid = \$12,126.24 - \$11,400$

STEP 16

Calculate the amount of interest Diane paid on the loan.
$Interest\, paid = \$12,126.24 - \$11,400 = \$726.24$
(b) The amount of interest Diane paid on the loan is $\$ 726.24$ .

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Diane bought $12,600\$ 12,600$12,600 in lab equipment, paying $1200\$ 1200$1200 down and taking out a loan for the rest. She paid $505.26\$ 505.26$505.26 monthly for 2 years to pay off the loan. (a) What was the total cost? (b) How much interest did she pay?

STEP 1

STEP 2

Calculate the amount Diane took out as a loan by subtracting the down payment from the total cost of the equipment.Loan amount=Total cost−Down paymentLoan\, amount = Total\, cost - Down\, paymentLoanamount=Totalcost−Downpayment

STEP 3

Plug in the given values to calculate the loan amount.Loan amount=$12,600−$1,200Loan\, amount = \$12,600 - \$1,200Loanamount=$12,600−$1,200

STEP 4

Calculate the loan amount.Loan amount=$12,600−$1,200=$11,400Loan\, amount = \$12,600 - \$1,200 = \$11,400Loanamount=$12,600−$1,200=$11,400

STEP 5

Calculate the total number of monthly payments Diane made over the 2 years.Total monthly payments=Number of years×12 months per yearTotal\, monthly\, payments = Number\, of\, years \times 12\, months\, per\, yearTotalmonthlypayments=Numberofyears×12monthsperyear

STEP 6

Plug in the values for the number of years to calculate the total number of monthly payments.Total monthly payments=2×12Total\, monthly\, payments = 2 \times 12Totalmonthlypayments=2×12

STEP 7

Calculate the total number of monthly payments.Total monthly payments=2×12=24Total\, monthly\, payments = 2 \times 12 = 24Totalmonthlypayments=2×12=24

STEP 8

STEP 9

Plug in the values for the monthly payment amount and the total number of monthly payments to calculate the total paid through monthly payments.Total paid through monthly payments=$505.26×24Total\, paid\, through\, monthly\, payments = \$505.26 \times 24Totalpaidthroughmonthlypayments=$505.26×24

STEP 10

Calculate the total paid through monthly payments.Total paid through monthly payments=$505.26×24=$12,126.24Total\, paid\, through\, monthly\, payments = \$505.26 \times 24 = \$12,126.24Totalpaidthroughmonthlypayments=$505.26×24=$12,126.24

STEP 11

STEP 12

Plug in the values for the down payment and the total paid through monthly payments to calculate the total amount paid.Total amount paid=$1,200+$12,126.24Total\, amount\, paid = \$1,200 + \$12,126.24Totalamountpaid=$1,200+$12,126.24

STEP 13

STEP 14

STEP 15

Plug in the values for the total paid through monthly payments and the loan amount to calculate the interest paid.Interest paid=$12,126.24−$11,400Interest\, paid = \$12,126.24 - \$11,400Interestpaid=$12,126.24−$11,400

STEP 16

Calculate the amount of interest Diane paid on the loan.Interest paid=$12,126.24−$11,400=$726.24Interest\, paid = \$12,126.24 - \$11,400 = \$726.24Interestpaid=$12,126.24−$11,400=$726.24(b) The amount of interest Diane paid on the loan is $726.24\$ 726.24$726.24.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Diane bought $\$ 12,600$ in lab equipment, paying $\$ 1200$ down and taking out a loan for the rest. She paid $\$ 505.26$ monthly for 2 years to pay off the loan. (a) What was the total cost? (b) How much interest did she pay?

Calculate the amount Diane took out as a loan by subtracting the down payment from the total cost of the equipment.
$Loan\, amount = Total\, cost - Down\, payment$

Plug in the given values to calculate the loan amount.
$Loan\, amount = \$12,600 - \$1,200$

Calculate the loan amount.
$Loan\, amount = \$12,600 - \$1,200 = \$11,400$

Calculate the total number of monthly payments Diane made over the 2 years.
$Total\, monthly\, payments = Number\, of\, years \times 12\, months\, per\, year$

Plug in the values for the number of years to calculate the total number of monthly payments.
$Total\, monthly\, payments = 2 \times 12$

Calculate the total number of monthly payments.
$Total\, monthly\, payments = 2 \times 12 = 24$

Plug in the values for the monthly payment amount and the total number of monthly payments to calculate the total paid through monthly payments.
$Total\, paid\, through\, monthly\, payments = \$505.26 \times 24$

Calculate the total paid through monthly payments.
$Total\, paid\, through\, monthly\, payments = \$505.26 \times 24 = \$12,126.24$

Plug in the values for the down payment and the total paid through monthly payments to calculate the total amount paid.
$Total\, amount\, paid = \$1,200 + \$12,126.24$

Plug in the values for the total paid through monthly payments and the loan amount to calculate the interest paid.
$Interest\, paid = \$12,126.24 - \$11,400$

Calculate the amount of interest Diane paid on the loan.
$Interest\, paid = \$12,126.24 - \$11,400 = \$726.24$
(b) The amount of interest Diane paid on the loan is $\$ 726.24$ .