Questions: Use PMT = (P(r/n))/(1-(1+(r/n))^(-nt)). Round to the nearest dollar. Suppose that you borrow 10,000 for four years at 6% toward the purchase of a car. Find the monthly payments and the total interest for the loan. A. 235 ; 11,280 B. 553 ; 16,544 C. 276 ; 13,248 D. 235 ; 1,280

Solution Steps

To find the monthly payments (PMT) for the loan, we will use the given formula for PMT, where \( P \) is the principal amount, \( r \) is the annual interest rate, \( n \) is the number of payments per year, and \( t \) is the number of years. After calculating the monthly payment, we can find the total payment over the loan period and subtract the principal to find the total interest paid.

Using the formula for monthly payment \( PMT \):

\[ PMT = \frac{P \left( \frac{r}{n} \right)}{1 - \left(1 + \frac{r}{n}\right)^{-nt}} \]

Substituting the values \( P = 10000 \), \( r = 0.06 \), \( n = 12 \), and \( t = 4 \):

\[ PMT = \frac{10000 \left( \frac{0.06}{12} \right)}{1 - \left(1 + \frac{0.06}{12}\right)^{-12 \cdot 4}} \approx 234.8503 \]

Rounding to the nearest dollar gives:

\[ \text{Monthly Payment} \approx 235 \]

The total payment over the loan period is calculated as:

\[ \text{Total Payment} = PMT \cdot n \cdot t = 235 \cdot 12 \cdot 4 \approx 11272.8139 \]

The total interest paid over the loan period is:

\[ \text{Total Interest} = \text{Total Payment} - P = 11272.8139 - 10000 \approx 1272.8139 \]

Rounding to the nearest dollar gives:

\[ \text{Total Interest} \approx 1273 \]

Final Answer