Math / Numbers & Operations

QuestionTo purchase $\$ 12,100$ worth of lab equipment for her business, Tammy made a down payment of $\$ 1600$ and took out a business loan for the rest. After 3 years of paying monthly payments of $\$ 319.44$ , she finally paid off the loan. (a) What was the total amount Tammy ended up paying for the equipment (including the down payment and monthly payments)? $\$$ Џl (b) How much interest did Tammy pay on the loan? $\$ \square$

Studdy Solution

STEP 1

1. Tammy's total cost for the lab equipment includes the down payment and the monthly payments over 3 years.
2. The total amount paid includes 36 monthly payments, each of $\$ 319.44$ .
3. The interest paid is the difference between the total amount paid and the original amount borrowed (loan principal).

STEP 2

1. Calculate the total amount Tammy paid for the equipment.
2. Calculate the total amount of the monthly payments.
3. Calculate the total interest paid on the loan.

STEP 3

Calculate the total amount Tammy paid for the equipment, including the down payment and the monthly payments.
First, calculate the total amount of the monthly payments: $\text{Total Monthly Payments} = 36 \times 319.44$

STEP 4

Multiply to find the total amount of the monthly payments:
$36 \times 319.44 = 11500.64$

STEP 5

Add the down payment to the total amount of the monthly payments to find the total amount paid for the equipment:
$\text{Total Amount Paid} = 1600 + 11500.64$

STEP 6

Perform the addition to find the total amount paid:
$1600 + 11500.64 = 13100.64$

STEP 7

Calculate the amount borrowed (loan principal):
$\text{Loan Principal} = 12100 - 1600$

STEP 8

Perform the subtraction to find the loan principal:
$12100 - 1600 = 10500$

STEP 9

Calculate the total interest paid on the loan by subtracting the loan principal from the total amount paid:
$\text{Total Interest Paid} = 13100.64 - 10500$

STEP 10

Perform the subtraction to find the total interest paid:
$13100.64 - 10500 = 2600.64$
Solution: (a) The total amount Tammy ended up paying for the equipment is $\$ 13100.64$ . (b) The total interest Tammy paid on the loan is $\$ 2600.64$ .

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Studdy Solution

STEP 1

STEP 2

1. Calculate the total amount Tammy paid for the equipment.
2. Calculate the total amount of the monthly payments.
3. Calculate the total interest paid on the loan.

STEP 3

Calculate the total amount Tammy paid for the equipment, including the down payment and the monthly payments.
First, calculate the total amount of the monthly payments: $\text{Total Monthly Payments} = 36 \times 319.44$

STEP 4

Multiply to find the total amount of the monthly payments:
$36 \times 319.44 = 11500.64$

STEP 5

Add the down payment to the total amount of the monthly payments to find the total amount paid for the equipment:
$\text{Total Amount Paid} = 1600 + 11500.64$

STEP 6

Perform the addition to find the total amount paid:
$1600 + 11500.64 = 13100.64$

STEP 7

Calculate the amount borrowed (loan principal):
$\text{Loan Principal} = 12100 - 1600$

STEP 8

Perform the subtraction to find the loan principal:
$12100 - 1600 = 10500$

STEP 9

Calculate the total interest paid on the loan by subtracting the loan principal from the total amount paid:
$\text{Total Interest Paid} = 13100.64 - 10500$

STEP 10

Perform the subtraction to find the total interest paid:
$13100.64 - 10500 = 2600.64$
Solution: (a) The total amount Tammy ended up paying for the equipment is $\$ 13100.64$ . (b) The total interest Tammy paid on the loan is $\$ 2600.64$ .

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Studdy Solution

STEP 1

STEP 2

1. Calculate the total amount Tammy paid for the equipment.2. Calculate the total amount of the monthly payments.3. Calculate the total interest paid on the loan.

STEP 3

Calculate the total amount Tammy paid for the equipment, including the down payment and the monthly payments.First, calculate the total amount of the monthly payments: Total Monthly Payments=36×319.44 \text{Total Monthly Payments} = 36 \times 319.44 Total Monthly Payments=36×319.44

STEP 4

Multiply to find the total amount of the monthly payments:36×319.44=11500.64 36 \times 319.44 = 11500.64 36×319.44=11500.64

STEP 5

Add the down payment to the total amount of the monthly payments to find the total amount paid for the equipment:Total Amount Paid=1600+11500.64 \text{Total Amount Paid} = 1600 + 11500.64 Total Amount Paid=1600+11500.64

STEP 6

Perform the addition to find the total amount paid:1600+11500.64=13100.64 1600 + 11500.64 = 13100.64 1600+11500.64=13100.64

STEP 7

Calculate the amount borrowed (loan principal):Loan Principal=12100−1600 \text{Loan Principal} = 12100 - 1600 Loan Principal=12100−1600

STEP 8

Perform the subtraction to find the loan principal:12100−1600=10500 12100 - 1600 = 10500 12100−1600=10500

STEP 9

Calculate the total interest paid on the loan by subtracting the loan principal from the total amount paid:Total Interest Paid=13100.64−10500 \text{Total Interest Paid} = 13100.64 - 10500 Total Interest Paid=13100.64−10500

STEP 10

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1. Calculate the total amount Tammy paid for the equipment.
2. Calculate the total amount of the monthly payments.
3. Calculate the total interest paid on the loan.

Calculate the total amount Tammy paid for the equipment, including the down payment and the monthly payments.
First, calculate the total amount of the monthly payments: $\text{Total Monthly Payments} = 36 \times 319.44$

Multiply to find the total amount of the monthly payments:
$36 \times 319.44 = 11500.64$

Add the down payment to the total amount of the monthly payments to find the total amount paid for the equipment:
$\text{Total Amount Paid} = 1600 + 11500.64$

Perform the addition to find the total amount paid:
$1600 + 11500.64 = 13100.64$

Calculate the amount borrowed (loan principal):
$\text{Loan Principal} = 12100 - 1600$

Perform the subtraction to find the loan principal:
$12100 - 1600 = 10500$

Calculate the total interest paid on the loan by subtracting the loan principal from the total amount paid:
$\text{Total Interest Paid} = 13100.64 - 10500$