Simple Interest
Match the time unit to the annual rate, then identify whether the question asks for interest or total amount.
Simple Interest
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Simple interest always uses the original principal
In simple interest, the amount earned each year stays constant because interest is calculated only from the original principal.
I = PrtA = P + I = P(1 + rt)Here, P is principal, r is the annual rate written as a decimal, t is time in years, I is interest, and A is the maturity value.
Match the units
If the rate is per year, convert months to a fraction of a year before substituting.
Interest is not the final amount
Interest is only the increase. Add it to principal when the question asks for maturity value or total repayment.
Use the formula as a relationship, not a memorized direction
Write I = Prt, circle the unknown, and divide by the other three factors when solving backward. For comparisons using the same principal, compare rate×time first.
Why it works
Simple interest varies directly with principal, annual rate, and time. Doubling any one of these while holding the others fixed doubles the interest.
Five forms you should recognize
Problem: Invest ₱12,000 at 5% simple interest for 3 years.
I = 12,000(0.05)(3) = ₱1,800Why: Each year earns 5% of the same ₱12,000 principal.
Problem: A ₱20,000 loan charges 6% for 2 years. Find total repayment.
I = 20,000(0.06)(2) = 2,400; A = ₱22,400Why: Repayment includes both principal and interest.
Problem: Find the interest on ₱15,000 at 8% for 9 months.
t = 912 = 0.75; I = 15,000(0.08)(0.75) = ₱900Why: An annual rate requires time measured in years.
Problem: ₱2,100 interest is earned at 7% for 3 years. Find P.
P = 2,100(0.07×3) = ₱10,000Why: Divide the known interest by rate×time.
Problem: Compare 6% for 3 years with 8% for 2 years using the same principal.
0.06(3) = 18%; 0.08(2) = 16%Why: With equal principals, the larger rate×time product earns more.
Check before you commit
- Using a percent as a whole number instead of a decimal
- Using months directly with an annual interest rate
- Reporting interest when the question asks for total repayment
- Subtracting interest from maturity value incorrectly when recovering principal
- Assuming a higher annual rate always earns more without comparing time
- Applying compound-growth reasoning to a simple-interest problem
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Simple Interest FAQ
What remains constant under simple interest?
The principal used to calculate interest remains the original principal, so equal periods earn equal interest.
How do I convert months into years?
Divide the number of months by 12.
How is maturity value different from interest?
Interest is the amount earned or charged; maturity value is principal plus interest.
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