What is the amount of interest on a loan of $$ \$ 5,000 $$, at $$ 10 \% $$ interest, for 278 days using the ordinary interest method. selectone Oa. $$ \$ 500 $$ ob. $$ \$ 1.80 $$ oc. $$ \$ 5.500 $$ od. $$ \$ 385.11 $$

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UpStudy AI · Accepted Answer

To calculate the amount of interest on a loan using the ordinary interest method, we can use the formula:

$$
I = P \times r \times t
$$

where:
- $$ I $$ is the interest,
- $$ P $$ is the principal amount (the initial loan amount),
- $$ r $$ is the annual interest rate (as a decimal),
- $$ t $$ is the time in years.

### Step 1: Identify the known values
- $$ P = 5000 $$
- $$ r = 10\% = 0.10 $$
- $$ t = \frac{278}{360} $$ (since the ordinary interest method uses a 360-day year)

### Step 2: Calculate $$ t $$
Now, let's calculate $$ t $$:

$$
t = \frac{278}{360}
$$

### Step 3: Calculate the interest $$ I $$
Now we can substitute the values into the interest formula:

$$
I = 5000 \times 0.10 \times t
$$

Let's calculate $$ t $$ and then $$ I $$.

I'll perform the calculations now.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{278}{360}$$
- step1: Reduce the fraction:
  $$\frac{139}{180}$$
Calculate or simplify the expression $$ 5000 * 0.10 * (278/360) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5000\times 0.1\left(\frac{278}{360}\right)$$
- step1: Reduce the fraction:
  $$5000\times 0.1\times \frac{139}{180}$$
- step2: Multiply the terms:
  $$500\times \frac{139}{180}$$
- step3: Reduce the numbers:
  $$25\times \frac{139}{9}$$
- step4: Multiply:
  $$\frac{25\times 139}{9}$$
- step5: Multiply:
  $$\frac{3475}{9}$$
### Step 2: Calculate $$ t $$
The value of $$ t $$ is:

$$
t = \frac{278}{360} \approx 0.7722
$$

### Step 3: Calculate the interest $$ I $$
Now substituting $$ t $$ into the interest formula:

$$
I = 5000 \times 0.10 \times 0.7722 \approx 386.11
$$

### Conclusion
The amount of interest on a loan of $$ \$ 5,000 $$ at $$ 10\% $$ interest for 278 days using the ordinary interest method is approximately $$ \$ 386.11 $$.

Thus, the correct answer is:
**od. $$ \$ 385.11 $$** (rounded to two decimal places).
The interest is approximately \$385.11.

What is the amount of interest on a loan of \( \$ 5,000 \), at \( 10 \% \) interest, for 278 days using the ordinary interest method. selectone Oa. \( \$ 500 \) ob. \( \$ 1.80 \) oc. \( \$ 5.500 \) od. \( \$ 385.11 \)

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