I need help with this I keep putting the numbers in wrong on the formula ! PLEASE HELP
Price of article = $315.50
Down payment = $31.55
Monthly payment amount = $16.50
Duration of payments = 20 months
True annual interest rate to the nearest tenth = %
Formula: I(Interest)= 2YC/M(N+1)
y = payments per year; c = total interest paid; m = amount financed; n = total number of payments.
Let's figure it this way.
315.5 - 31,55 = 283.95 >> amount financed
16.5 * 20 = 330 >> amount paid
330 - 283.95 = 46.05 >> interest
46.05 / 283.95 = 0.16217 = 16.2% >> interest rate
Please ignore my previous post. I goofed!
I = PRT
46.05 = 283.95 * R * 1.6667
46.05 = 473.26R
46.04 / 473.26 = R
0.0972 = 9.7% = R
To find the true annual interest rate, you can use the formula:
I(Interest) = (2 * Y * C) / (M * (N + 1))
Let's plug in the given values:
Y = 12 (since there are 12 payments in a year)
C = Unknown (this is what we need to find)
M = Price of the article - Down payment = $315.50 - $31.55 = $283.95
N = Duration of payments = 20 months
The formula can now be written as:
I = (2 * 12 * C) / (283.95 * (20 + 1))
We can simplify this equation further:
I = (24C) / (5886.45)
To solve for C, we need to rearrange the formula:
C = (I * 5886.45) / 24
Sure, I'd be happy to help you with this! To calculate the true annual interest rate, we'll need to use the formula you provided: I(Interest) = 2YC / M(N + 1).
Let's plug in the values you have:
Y = 12 (since there are 12 months in a year)
C = ? (unknown, we'll need to solve for this)
M = $315.50 - $31.55 = $283.95 (the amount financed, which is the price of the article minus the down payment)
N = 20 (the total number of payments)
To solve for C, we need to know the total interest paid. We can calculate this by multiplying the monthly payment amount by the number of payments and subtracting the amount financed. Let's do the math:
Total interest paid = (monthly payment amount * total number of payments) - amount financed
Total interest paid = ($16.50 * 20) - $283.95
Total interest paid = $330 - $283.95
Total interest paid = $46.05
Now that we've found the value of C, let's put it in the formula along with the other values:
I(Interest) = 2 * 12 * $46.05 / $283.95 * (20 + 1)
Now we can simplify the equation:
I(Interest) = 24 * $46.05 / $283.95 * 21
I(Interest) = $1,104.60 / $5,972.95
I(Interest) ≈ 0.1846
To get the true annual interest rate to the nearest tenth, we multiply the result by 100 and round to one decimal place:
True annual interest rate = 0.1846 * 100 ≈ 18.5%
Therefore, the true annual interest rate for this loan is approximately 18.5%.