Help! My friend let me borrow their notes and I don't know how they got these answers because they didn't show their work. Could someone please help me? *The answers are correct btw.
David is flying from Detroit to Las Vegas. The airfare is $476. He can afford monthly payments of $40. The loan is charged 6.7% completely daily. (Show your work)
A) Determine the number of payments that must be made
B) What is the total amount paid back.
C) How much was paid in interest charges?
A) 13
B) $493.97
C) 17.97
"The loan is charged 6.7% completely daily"
This makes no sense, did you mean compounded daily ?
If so, then this question is quite difficult. The Present Value formula of an annuity assumes that the time period of the payment and the time period of the compounding are the same.
Come back with your corrections.
My bad *compounded daily
To determine the number of payments that must be made, you can divide the total airfare ($476) by the monthly payment amount ($40). This will give you the number of months it will take to pay off the loan. However, since the loan is charged completely daily, you need to convert the monthly payment to a daily payment by dividing $40 by the average number of days in a month.
Let's calculate the number of payments:
1. Convert the monthly payment to a daily payment:
Avg. number of days in a month = 365 days / 12 months = 30.42 days (approx.)
Daily payment = $40 / 30.42 days ≈ $1.31 (approx.)
2. Divide the total airfare by the daily payment:
Total number of payments = $476 / $1.31 ≈ 363.36 (approx.)
Since you can't have a fraction of a payment, you need to round up to the nearest whole number of payments. Therefore, the number of payments that must be made is 364 or approximately 13 payments (as mentioned in the answer provided).
To calculate the total amount paid back, multiply the number of payments (13) by the monthly payment amount ($40):
Total amount paid back = 13 * $40 = $520.
The answer provided in the notes, $493.97, is incorrect. It should be $520.
To calculate the interest charges, subtract the total airfare ($476) from the total amount paid back ($520):
Interest charges = $520 - $476 = $44.
The answer provided in the notes, $17.97, is incorrect. It should be $44.
Therefore, based on the correct calculations:
A) The number of payments that must be made is 13 (as stated in the answer).
B) The total amount paid back is $520 (not $493.97).
C) The interest charges amount to $44 (not $17.97).