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QuestionA family bought a jet ski for \$7,500 with a 10% down payment. What are the monthly installments at 696 simple interest for 12 months? Options: \$578.50, \$586.75, \$596.25, \$601.00, None of these choices.

Studdy Solution

STEP 1

Assumptions1. The cost of the jet ski is $7,500. The down payment is10% of the cost3. The remaining balance is financed at a simple interest rate of6%
4. The loan is to be repaid in12 equal monthly installments5. The interest is calculated as a one-time payment, not monthly compounding6. Both the principal amount and interest must be equally divided among the12 months

STEP 2

First, we need to find the down payment amount. We can do this by multiplying the cost of the jet ski by the down payment rate.
Down payment=Cost of jet skitimesDown payment rateDown\, payment = Cost\, of\, jet\, ski \\times Down\, payment\, rate

STEP 3

Now, plug in the given values for the cost of the jet ski and down payment rate to calculate the down payment.
Down payment=$7,500times10%Down\, payment = \$7,500 \\times10\%

STEP 4

Convert the percentage to a decimal value.
10%=0.110\% =0.1Down payment=$7,500times0.1Down\, payment = \$7,500 \\times0.1

STEP 5

Calculate the down payment amount.
Down payment=$7,500times0.1=$750Down\, payment = \$7,500 \\times0.1 = \$750

STEP 6

Now that we have the down payment amount, we can find the financed amount. This is the cost of the jet ski minus the down payment.
Financed amount=Cost of jet ski−Down paymentFinanced\, amount = Cost\, of\, jet\, ski - Down\, payment

STEP 7

Plug in the values for the cost of the jet ski and the down payment to calculate the financed amount.
Financed amount=$7,500−$750Financed\, amount = \$7,500 - \$750

STEP 8

Calculate the financed amount.
Financed amount=$7,500−$750=$6,750Financed\, amount = \$7,500 - \$750 = \$6,750

STEP 9

Now, we need to find the interest amount on the financed sum. We can do this by multiplying the financed amount by the interest rate.
Interest=Financed amounttimesInterest rateInterest = Financed\, amount \\times Interest\, rate

STEP 10

Now, plug in the given values for the financed amount and interest rate to calculate the interest.
Interest=$6,750times6%Interest = \$6,750 \\times6\%

STEP 11

Convert the percentage to a decimal value.
6%=0.066\% =0.06Interest=$6,750times0.06Interest = \$6,750 \\times0.06

STEP 12

Calculate the interest amount.
Interest=$6,750times0.06=$405Interest = \$6,750 \\times0.06 = \$405

STEP 13

Now that we have the interest amount, we can find the total amount the family has to pay back. This includes both the financed amount and the interest.
Total amount=Financed amount+InterestTotal\, amount = Financed\, amount + Interest

STEP 14

Plug in the values for the financed amount and the interest to calculate the total amount.
Total amount=$6,750+$405Total\, amount = \$6,750 + \$405

STEP 15

Calculate the total amount the family has to pay back.
Total amount=$,750+$405=$7,155Total\, amount = \$,750 + \$405 = \$7,155

STEP 16

Now that we have the total amount the family has to pay back, we can divide this by the number of months (12) to find the amount they need to pay each month.
Monthly payment=Total amount/Number of monthsMonthly\, payment = Total\, amount / Number\, of\, months

STEP 17

Plug in the values for the total amount and the number of months to calculate the monthly payment.
Monthly payment=$7,155/12Monthly\, payment = \$7,155 /12

STEP 18

Calculate the monthly payment amount.
Monthly payment=$7,155/12=$596.25Monthly\, payment = \$7,155 /12 = \$596.25The family needs to pay $596.25 each month.

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