Question

Find the total amount owed, to the nearest cent, for a simple interest loan with a principal of $2950, an interest rate of 7.4% and a time period of 1.5 years. Show your work.

Answer 1

To calculate the total amount owed for a simple interest loan, we can use the formula for simple interest:

\[
I = P \times r \times t
\]

where:
- \(I\) is the interest accrued,
- \(P\) is the principal amount (the initial amount of the loan),
- \(r\) is the annual interest rate (as a decimal),
- \(t\) is the time the money is borrowed for (in years).

Given:
- \(P = 2950\)
- \(r = 7.4\% = 0.074\)
- \(t = 1.5\)

First, we calculate the interest (\(I\)):

\[
I = 2950 \times 0.074 \times 1.5
\]

Calculating step by step:

1. Multiply the principal by the interest rate:
\[
2950 \times 0.074 = 218.3
\]

2. Now multiply this result by the time period (1.5 years):
\[
I = 218.3 \times 1.5 = 327.45
\]

Now that we have calculated the interest, we can find the total amount owed by adding the interest to the principal:

\[
\text{Total Amount Owed} = P + I = 2950 + 327.45
\]

Calculating this:

\[
\text{Total Amount Owed} = 2950 + 327.45 = 3277.45
\]

Therefore, the total amount owed, rounded to the nearest cent, is:

\[
\boxed{3277.45}
\]