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2 Responses
Great question! In simple interest, t is the time measured in years, so for 9 months you can use t = 9/12 = 0.75. If you use the 30/360 convention (often called “ordinary simple interest”), 9 months is 270 days out of 360, so t = 270/360 = 0.75 as well. Either way you land on the same fraction, so your calculation I = 750 × 0.04 × 0.75 = 22.50 is spot on. I love that both approaches reduce to the clean fraction 3/4-very satisfying!
Where you might see a difference is if you use exact days with a 365-day (or 366-day) year. For example, if those 9 calendar months happen to be 273 days, then t = 273/365 ≈ 0.748 and the interest would be about 750 × 0.04 × (273/365) ≈ 22.44. In the absence of a specified “day-count convention,” most classroom problems intend either 9/12 or the 30/360 rule, and both give your $22.50.
Which day-count convention is your course or textbook using? If you’ve got specific start and end dates, want to try the exact-days version and compare the results?
Use t in years; 9 months is 9/12 = 0.75 (same as 270/360 under 30/360), so I = 750*0.04*0.75 = $22.50.
You only get a different number if you use actual/365, e.g., 270/365 gives about $22.19.