Interest Calculator
Calculate simple and compound interest on savings, investments, and loans. See how your money grows over time.
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Quick Answer: Interest Formulas
Simple Interest: I = P × R × T | Compound Interest: A = P(1 + r/n)^(nt)
Dr. Snezana Lawrence
Mathematical Historian
15+ years experience
PhD from Yale University. Published mathematical historian ensuring precision in all calculations.
Education
PhD in Mathematical History - Yale University
Table of Contents
Simple vs Compound Interest
Simple Interest
Interest calculated only on the original principal amount. The interest earned remains constant each period.
- Linear growth over time
- Used for short-term loans
- Easier to calculate
Compound Interest
Interest calculated on both principal and accumulated interest. "Interest on interest" leads to exponential growth.
- Exponential growth over time
- Used for savings/investments
- More profitable long-term
Interest Formulas
Simple Interest Formula
I = P × R × T
Compound Interest Formula
A = P(1 + r/n)nt
Compounding Frequency
How often interest compounds affects total earnings. More frequent = more interest:
| Frequency | Times/Year | $10,000 @ 5% for 10 yrs |
|---|---|---|
| Annually | 1 | $16,288.95 |
| Semi-annually | 2 | $16,386.16 |
| Quarterly | 4 | $16,436.19 |
| Monthly | 12 | $16,470.09 |
| Daily | 365 | $16,486.65 |
| Continuous | e | $16,487.21 |
Frequently Asked Questions
What is the formula for simple interest?
Simple Interest = Principal × Rate × Time. For example, $1,000 at 5% for 3 years = $1,000 × 0.05 × 3 = $150 interest.
What is compound interest?
Compound interest is interest calculated on both the initial principal and accumulated interest. It grows faster than simple interest because you earn "interest on interest."
How often should interest compound?
More frequent compounding means more interest earned. Daily compounding earns more than monthly, which earns more than annually. For savings, look for accounts that compound daily.
What is APY vs APR?
APR (Annual Percentage Rate) is the simple interest rate. APY (Annual Percentage Yield) includes compound interest, showing actual earnings. APY is always higher than APR when interest compounds.
How does the Rule of 72 work?
The Rule of 72 estimates how long it takes to double your money. Divide 72 by the interest rate. At 8%, money doubles in about 72 ÷ 8 = 9 years.
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Dr. Snezana Lawrence
Mathematical Historian | PhD from Yale
Dr. Lawrence is a published mathematical historian with a PhD from Yale University. She ensures mathematical precision and accuracy in all our calculations, conversions, and academic score calculators. Her expertise spans computational mathematics and educational assessment.
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