Diego Cruz decided to buy a used boat since his credit union was offering such low interest rates. He borrowed $3,100 at 3.75% on December 26, 2024, and paid it off May 5, 2026. How much did he pay in interest? (Assume ordinary interest and no leap year.) (Use Days in a year table.) Note: Do not round intermediate calculations. Round your answer to the nearest cent.
Answer (2)
To calculate the interest Diego paid on the loan, we will use the ordinary interest method, which assumes a 360-day year.
Step 1: Calculate the number of days between the borrowing and payoff dates.
Diego borrowed the money on December 26, 2024, and paid it off on January 5, 2026.
From December 26, 2024, to December 26, 2025, is 360 days.
December 26, 2025, to January 5, 2026, is 10 days.
Total number of days: 360 + 10 = 370 days.
Step 2: Calculate the ordinary interest.
The formula to calculate ordinary interest is:
I = 360 P × R × T
where:
I is the interest.
P is the principal amount borrowed, which is $3,100.
R is the annual interest rate, which is 3.75% (or 0.0375 as a decimal).
T is the time in days, which is 370.
Substitute these values into the formula:
I = 360 3100 × 0.0375 × 370
I = 360 43012.5
I ≈ 119.48
So, Diego paid approximately $119.48 in interest.
Therefore, the interest paid by Diego is $119.48. Ensure to round to the nearest cent as required.
Diego paid approximately $102.87 in interest on his loan, calculated using the ordinary interest method. This was determined over a total of 490 days from the loan's start to finish. The formula used takes into account the principal amount, interest rate, and the number of days the loan was held.
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