To calculate the monthly interest, take the APR and divide it by 360, then multiply the result by 30 days. Typically, each loan is backed by the vehicle that was purchased, hence we will utilize the secured APR.
8. For an average secured APR of 5.85%, the calculation is: 5.85% divided by 360 multiplied by 30 gives a monthly rate of 0.4875%.
The vehicle cost is 19,725; with a sales tax of 4.75% and a down payment of 2,175.
19,725 multiplied by 1.0475 results in 20,661.94, and after subtracting the down payment, the loan amount is 18,486.94.
To find the accrued interest for the first month: 18,486.94 multiplied by 0.4875% equals 90.12.
9. An excellent secured APR of 4.80% results in a monthly rate of 0.40% when 4.80% is divided by 360 and multiplied by 30.
Price of a different vehicle: 15,867; a sales tax of 5.25%; down payment equals 10% of the total.
Calculating, 15,867 multiplied by 1.0525 gives 16,700.02; taking 90% results in a principal balance of 15,030.02 at the loan's beginning.
10. For a fair secured APR at 7%, dividing by 360 and multiplying by 30 provides a monthly rate of 0.5833%.
Cost of a new vehicle is 19,072; sales tax stands at 4.5%; down payment of 1,200.
Cost for a used vehicle is 15,365; same tax and down payment as the new one.
Calculating for new: 19,072 multiplied by 1.045 results in 19,930.24, with down payment deducted gives 18,730.24.
Accrued interest for new is 18,730.24 multiplied by 0.5833% equating to 109.25.
For the used vehicle: 15,365 multiplied by 1.045 results in 16,056.43, then down payment leaves 14,856.43.
Accrued interest here is 14,856.43 multiplied by 0.5833% equaling 86.66.
The difference in interest accrued by the first month's end is 109.25 minus 86.66, which is 22.59.
Answer:
The rotation angle measures 2.11 °
Step-by-step explanation:
Stated as follows:
The radius of the circular path = r = 18 feet
The distance rolled by the wheel = l = 38 feet
Let us denote the angle of rotation as Ф
Now, according to the problem:
∵ the length of an arc at the center corresponds to an angle Ф
Thus,
distance rolled by the wheel = π × radius × 
As 180° represents π radians
And π approximates to 3.14
Thus, distance rolled by the wheel = 180 °× radius ×
That is l = r × Ф
So, Ф = 
Consequently, Ф = 
Therefore, Ф = 2.11 °
Thus, the rotation angle is Ф = 2.11 °
Hence, the rotation angle is 2.11 ° Answer
Answer: Initially, he had 27 sweets.
Step-by-step explanation: The most logical approach is to work backwards from what remained after the third day to the start of the first day.
On the third day, he consumed one-third of his sweets and was left with 8. If we let the total sweets on day three be denoted as a, then one-third of a equals what he ate and the two-thirds left equals 8, giving us:
8/a = 2/3
By cross-multiplying, we find:
8 x 3 = 2a
Therefore, 24 = 2a
This leads to a = 12.
Let the sweets on day two be represented as b. If he consumed one-third of b and was left with 12, we have the same structure; hence:
12/b = 2/3
Cross-multiplying gives:
12 x 3 = 2b
So, 36 = 2b, leading to b = 18.
Denote the number of sweets on day one as x. If one-third of x was eaten and 18 remained, we can set up the equation:
18/x = 2/3
Again, cross-multiplying results in:
18 x 3 = 2x
Which simplifies to 54 = 2x, yielding x = 27.
Thus, Tim received 27 sweets at the start.
