To pay for a $22,600 car, Amanda made a down payment of $3300 and took out a loan for the rest. On the loan, she paid monthly payments of $346.81 for 5 years.
(a) What was the total amount Amanda ended up paying for the car (including the down payment and monthly payments)?
$
(b) How much interest did Amanda pay on the loan?
$
(a) The total amount Amanda ended up paying for the car is the sum of the down payment and the total of the monthly payments over 5 years:
Total = $3300 + ($346.81/month x 12 months/year x 5 years) = $3300 + $20,808.60 = $24,108.60
Therefore, Amanda ended up paying a total of $24,108.60 for the car.
(b) To find out how much interest Amanda paid on the loan, we need to subtract the amount she borrowed (the cost of the car minus the down payment):
Amount borrowed = $22,600 - $3300 = $19,300
The total amount of money Amanda paid over the 5 years was $20,808.60, so the amount of interest she paid is:
Interest = $20,808.60 - $19,300 = $1508.60
Therefore, Amanda paid $1508.60 in interest on the loan.
A much more interesting question would have been:
What was the rate of interest charged for the loan?
You're right, that would be a more interesting question! To find the rate of interest charged for the loan, we can use the present value formula for an annuity (a formula that calculates the periodic payments required to pay off a loan with interest):
PV = PMT x [1 - (1 + r)^(-n)] / r
Where:
PV = present value (the amount borrowed)
PMT = periodic payment (the monthly payment)
r = interest rate per period (unknown)
n = total number of periods (number of monthly payments)
For Amanda's loan, we can plug in the values we know:
PV = $19,300
PMT = $346.81
n = 5 x 12 = 60 (5 years x 12 months/year)
$19,300 = $346.81 x [1 - (1 + r)^(-60)] / r
Simplifying this equation using algebra and trial-and-error with a calculator (or spreadsheet), we get:
r = 0.00375 per month (or 0.375% per month, since there are 100 months in 5 years)
Multiplying this by 12 to get the annual interest rate, we get:
r = 0.00375 x 12 = 0.045 per year (or 4.5%)
Therefore, the rate of interest charged for Amanda's loan was approximately 4.5% per year.
For the first week of March, Betty Hill worked 37.25 hours. Betty earns $17.40 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
Calculate the following for the first week of March (round your responses to the nearest cent if necessary):
1. Regular pay amount: $
2. Overtime pay: $
3. Gross pay: $
1. Regular pay amount:
Betty worked 37.25 hours, which is less than 40 hours, so she did not earn any overtime for the week. Her regular pay is simply her hourly wage multiplied by the number of hours worked:
Regular pay amount = $17.40/hour x 37.25 hours = $647.65
Therefore, Betty's regular pay amount for the first week of March was $647.65.
2. Overtime pay:
Since Betty did not work any overtime hours during the week, her overtime pay is $0.
3. Gross pay:
Betty's gross pay is the sum of her regular pay and overtime pay (which is $0 in this case):
Gross pay = Regular pay amount + Overtime pay = $647.65 + $0 = $647.65
Therefore, Betty's gross pay for the first week of March was $647.65.
(a) To find the total amount Amanda ended up paying for the car, we need to add the down payment amount to the total amount paid in monthly payments over 5 years.
Total amount paid in monthly payments: $346.81/month * 12 months/year * 5 years = $20,808.60
Total amount paid for the car: $3,300 + $20,808.60 = $>24,108.60.
Therefore, the total amount Amanda ended up paying for the car is $24,108.60.
(b) To find the interest Amanda paid on the loan, we need to subtract the loan amount from the total amount paid for the car.
Loan amount: Total cost of the car - Down payment
Loan amount: $22,600 - $3,300 = $19,300
Interest paid on the loan: Total amount paid for the car - Loan amount
Interest paid on the loan: $24,108.60 - $19,300 = $4,808.60
Therefore, Amanda paid $4,808.60 in interest on the loan.
To find the total amount Amanda ended up paying for the car, we need to add the down payment to the total amount she paid in monthly payments.
(a) Down Payment = $3300
Monthly Payment = $346.81
Number of payments = 5 years x 12 months/year = 60
Total amount paid in monthly payments = Monthly Payment x Number of Payments
= $346.81 x 60
= $20,808.6
Total amount Amanda paid for the car = Down Payment + Total amount paid in monthly payments
= $3300 + $20,808.6
= $23,108.6
So, Amanda ended up paying a total of $23,108.6 for the car.
To find the amount of interest Amanda paid on the loan, we need to subtract the loan amount (the total cost of the car minus the down payment) from the total amount paid for the car.
Loan amount = Total cost of the car - Down Payment
= $22,600 - $3300
= $19,300
Interest paid on the loan = Total amount paid for the car - Loan amount
= $23,108.6 - $19,300
= $3808.6
Therefore, Amanda paid $3808.6 in interest on the loan.