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3 Responses
Great question! I love this because it’s like asking, “Do I have to slice the pizza to eat it, or can I just take a big bite?” With simple interest, the key is: match the time unit to the rate’s unit. If the rate is per year (which it almost always is), then use time in years in I = P·r·t. Simple interest grows in a straight line-no stacking on top of itself-so whether you treat 18 months as 1.5 years or as 18 one-month chunks, you’ll land in the same place as long as you convert the rate correctly.
Worked example: P = 600, r = 5% = 0.05 per year, t = 18 months = 1.5 years. Interest = 600 × 0.05 × 1.5 = 45, so the total is 600 + 45 = 645. If you go month-by-month, the monthly rate is 0.05/12, so each month’s interest is 600 × (0.05/12) = 2.50. Over 18 months, that’s 2.50 × 18 = 45-same answer. The only time you’d get a different result is if the problem says “compounded monthly,” because then each month’s interest gets added to the principal before the next month. But for simple interest, 1.5 years or 18 months (with r/12) are just two equally good roads to the same destination.
For simple interest, the key is to match the units for the rate and the time. If the 5% is an annual rate, then in I = P·r·t you should take r = 0.05 per year and t in years. For 18 months, t = 18/12 = 1.5, so I = 600 × 0.05 × 1.5 = 45, giving a total of 645. Doing it month-by-month can give the same result if you convert the annual rate to a monthly rate r/12 and keep applying interest only to the original principal (not to a growing balance): I = 600 × (0.05/12) × 18 = 45 again. These match because simple interest is linear-there’s no compounding. The only time you’d get a different answer is if interest were compounded monthly, in which case the total would be slightly higher. Would you like to compare this with the compounded monthly case to see the difference?
I like to break time into little monthly ticks for simple interest, so I’d use I = P*(r/12)*m; for $600 at 5% over 18 months that’s I = 600*(0.05/12)*18 ≈ $37.50, so about $637.50 total-I think that’s right, but I might be mixing something up.
Example: 12 months would be 600*(0.05/12)*12 ≈ $30.