Math  /  Numbers & Operations

Question20. Jessica had to take her cat to the vet for emergency surgery which cost $400.00\$ 400.00. She doesn't have the cash to pay right now but expects to be able to pay off any loan in 30 days. Here are her options for payment: - She can pay in instalments. The vet will let her make monthly payments of $100.00\$ 100.00 for 4 months plus an administration fee of $20.00\$ 20.00. - She can borrow the money from her bank on her personal line of credit at an interest rate of 8%8 \% per annum. - She can get a payday loan at an interest rate of 1%1 \% per day. a. Calculate the total cost of each payment option. Show FSS and clearly indicate which option is which.

Studdy Solution

STEP 1

1. Jessica needs to pay a total of \$400 for the surgery.
2. She has three payment options: installment payments with a fee, a personal line of credit, and a payday loan.
3. The installment option includes a fixed administration fee.
4. The personal line of credit has an annual interest rate.
5. The payday loan has a daily interest rate.

STEP 2

1. Calculate the total cost for the installment payment option.
2. Calculate the total cost for the personal line of credit option.
3. Calculate the total cost for the payday loan option.
4. Compare the total costs to determine the least expensive option.

STEP 3

Calculate the total cost for the installment payment option.
The installment payment option involves: - Monthly payments of \$100 for 4 months. - An administration fee of \$20.
Total cost for installment payments: 4×100+20=400+20=420 4 \times 100 + 20 = 400 + 20 = 420

STEP 4

Calculate the total cost for the personal line of credit option.
The personal line of credit has an interest rate of 8%8\% per annum. Since Jessica plans to pay off the loan in 30 days, we need to calculate the interest for 30 days.
Convert the annual interest rate to a daily rate: Daily interest rate=8%365=0.08365 \text{Daily interest rate} = \frac{8\%}{365} = \frac{0.08}{365}
Calculate the interest for 30 days: Interest=400×(0.08365)×30 \text{Interest} = 400 \times \left(\frac{0.08}{365}\right) \times 30
Calculate the total cost: Total cost=400+Interest \text{Total cost} = 400 + \text{Interest}

STEP 5

Calculate the interest for 30 days:
Interest=400×(0.08365)×30=400×0.000219178×302.63 \text{Interest} = 400 \times \left(\frac{0.08}{365}\right) \times 30 = 400 \times 0.000219178 \times 30 \approx 2.63
Calculate the total cost: Total cost=400+2.63=402.63 \text{Total cost} = 400 + 2.63 = 402.63

STEP 6

Calculate the total cost for the payday loan option.
The payday loan has an interest rate of 1%1\% per day.
Calculate the interest for 30 days: Interest=400×0.01×30 \text{Interest} = 400 \times 0.01 \times 30
Calculate the total cost: Total cost=400+Interest \text{Total cost} = 400 + \text{Interest}

STEP 7

Calculate the interest for 30 days:
Interest=400×0.01×30=400×0.3=120 \text{Interest} = 400 \times 0.01 \times 30 = 400 \times 0.3 = 120
Calculate the total cost: Total cost=400+120=520 \text{Total cost} = 400 + 120 = 520

STEP 8

Compare the total costs of each option:
- Installment payments: \$420 - Personal line of credit: \$402.63 - Payday loan: \$520
The least expensive option is the personal line of credit at \$402.63.
The total costs for each payment option are: - Installment payments: $420\$420 - Personal line of credit: $402.63\$402.63 - Payday loan: $520\$520
The least expensive option is the personal line of credit.

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