To calculate the amount of interest on this loan, we’ll use the simple interest formula:

$I = P \times r \times \frac{t}{365}$

where:

• $I$ = interest,
• $P$ = principal amount (initial loan amount),
• $r$ = annual interest rate,
• $t$ = time in days,
• and 365 is used because the exact interest method typically assumes a 365-day year.

Given:

• $P = 4000$,
• $r = 0.13$ (or 13% as a decimal),
• $t = 160$ days.

Step-by-Step Calculation

1. Convert the interest rate to decimal form: $r = \frac{13}{100} = 0.13$

2. Substitute the values into the formula: $I = 4000 \times 0.13 \times \frac{160}{365}$

3. Calculate the interest: $I = 4000 \times 0.13 \times 0.43836 \approx 228.91$

So, the amount of interest on the loan is approximately $228.91.

Would you like a breakdown of any steps, or have other questions?

Related Questions

1. What would the interest be if the loan term was 180 days instead of 160 days?
2. How would the interest amount change if the interest rate was 10% instead of 13%?
3. What is the formula for calculating interest using the "ordinary interest" (360-day year) method?
4. How does compound interest differ from simple interest in loan calculations?
5. If the loan principal were increased to $5,000, what would be the new interest amount for 160 days?

Tip

For short-term loans, using the exact interest method (365 days) gives a slightly more accurate result than using the ordinary interest method (360 days).