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QuestionJuan bought a \$ 16,100 truck, paid \$ 4,100 down, and took a loan with \$ 265.62 monthly for 4 years. Find: (a) Total cost of the truck. (b) Interest paid on the loan.

Studdy Solution

STEP 1

Assumptions1. The cost of the truck is 16,100.ThedownpaymentmadebyJuanis16,100. The down payment made by Juan is 4,1003. The rest of the amount is paid through a loan4. The monthly payments for the loan are $265.625. The loan is paid over a period of4 years6. The total amount paid for the truck includes both the down payment and the monthly payments7. The interest paid on the loan is the difference between the total amount paid and the original cost of the truck

STEP 2

First, we need to find the loan amount. We can do this by subtracting the down payment from the cost of the truck.
Loan amount=Cost of the truck−Down paymentLoan\, amount = Cost\, of\, the\, truck - Down\, payment

STEP 3

Now, plug in the given values for the cost of the truck and the down payment to calculate the loan amount.
Loan amount=$16,100−$,100Loan\, amount = \$16,100 - \$,100

STEP 4

Calculate the loan amount.
Loan amount=$16,100−$4,100=$12,000Loan\, amount = \$16,100 - \$4,100 = \$12,000

STEP 5

Next, we need to find the total amount paid for the loan. We can do this by multiplying the monthly payments by the number of months.
Total loan payment=Monthly paymentstimesNumber of monthsTotal\, loan\, payment = Monthly\, payments \\times Number\, of\, months

STEP 6

Since the loan was paid over a period of4 years, the number of months is4 years times12 months/year.
Number of months=4 yearstimes12 months/year=48 monthsNumber\, of\, months =4\, years \\times12\, months/year =48\, months

STEP 7

Now, plug in the given values for the monthly payments and the number of months to calculate the total loan payment.
Total loan payment=$265.62times48Total\, loan\, payment = \$265.62 \\times48

STEP 8

Calculate the total loan payment.
Total loan payment=$265.62times48=$12,749.76Total\, loan\, payment = \$265.62 \\times48 = \$12,749.76

STEP 9

Now that we have the total loan payment, we can find the total amount Juan paid for the truck. This includes both the down payment and the total loan payment.
Total amount paid=Down payment+Total loan paymentTotal\, amount\, paid = Down\, payment + Total\, loan\, payment

STEP 10

Plug in the values for the down payment and the total loan payment to calculate the total amount paid.
Total amount paid=$4,100+$12,749.76Total\, amount\, paid = \$4,100 + \$12,749.76

STEP 11

Calculate the total amount paid.
Total amount paid=$4,100+$,749.76=$16,849.76Total\, amount\, paid = \$4,100 + \$,749.76 = \$16,849.76(a) Juan ended up paying $16,849.76 for the truck.

STEP 12

Finally, we need to find the interest paid on the loan. We can do this by subtracting the original loan amount from the total loan payment.
Interest=Total loan payment−Original loan amountInterest = Total\, loan\, payment - Original\, loan\, amount

STEP 13

Plug in the values for the total loan payment and the original loan amount to calculate the interest.
Interest=$12,749.76−$12,000Interest = \$12,749.76 - \$12,000

STEP 14

Calculate the interest paid.
Interest=$12,749.76−$12,000=$749.76Interest = \$12,749.76 - \$12,000 = \$749.76(b) Juan paid $749.76 in interest on the loan.

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