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= %
P = 315.50
dp = 31.55
mpa = 16.50
n = 20
315.50 -31.55 = 283.95
Mpa * n
16.50 * 20 = 330
Interest = 330-283.95
Interest = 46.05
rate = 46.05/283.95
To find the true annual interest rate, we can use the formula:
\(I = \frac{P - D}{D \cdot n}\)
Where:
P = Price of the article
D = Down payment
n = Duration of payments
Given values:
Article price (P) = $315.50
Down payment (D) = $31.55
Monthly payment amount = $16.50
Duration of payments (n) = 20 months
Let's substitute the given values into the equation:
\(I = \frac{315.50 - 31.55}{31.55 \cdot 20}\)
\(I = \frac{283.95}{631}\)
Now let's calculate the division:
\(I \approx 0.449..\)
To convert this decimal to a percentage, we can multiply it by 100:
\(I \approx 0.449.. \times 100\)
Thus, the true annual interest rate to the nearest tenth percent is approximately 44.9%.
To find the true annual interest rate, we'll need to use the formula for calculating the interest rate:
Interest Rate (in decimal form) = (Total Interest Paid / Total Amount of Loan) / Duration of Payments
First, let's calculate the total amount of the loan by subtracting the down payment from the price of the article:
Total Amount of Loan = Price of Article - Down Payment
Total Amount of Loan = $315.50 - $31.55
Total Amount of Loan = $283.95
Next, let's calculate the total interest paid over the duration of the payments:
Total Interest Paid = Monthly Payment Amount * Duration of Payments - Total Amount of Loan
Total Interest Paid = $16.50 * 20 - $283.95
Total Interest Paid = $330 - $283.95
Total Interest Paid = $46.05
Now we can calculate the interest rate:
Interest Rate (in decimal form) = ($46.05 / $283.95) / 20
To convert the decimal form to a percentage, we multiply by 100:
Interest Rate (in decimal form) = ($46.05 / $283.95) / 20 * 100
Calculating this expression gives us:
Interest Rate (in decimal form) = 0.003217
Now, let's convert this decimal to a percentage by multiplying by 100:
Interest Rate (in percentage form) = 0.003217 * 100
Rounding this to the nearest tenth, we get:
Interest Rate (in percentage form) ≈ 0.32%
Therefore, the true annual interest rate to the nearest tenth is 0.3%.