Formula & Methodology
Simple Interest
Interest = Principal × Rate × Time Interest is calculated only on the original principal. Unlike compound interest, previously earned interest does not generate additional interest.
Total Amount
Total = Principal + (Principal × Rate × Time) The total repayment or maturity value equals the original principal plus all accrued simple interest.
Daily Simple Interest
Daily Interest = Principal × (Annual Rate ÷ 365) × Days Many auto loans and some personal loans use daily simple interest, where interest accrues each day on the outstanding principal balance.
Key Terms
- Principal
- The original amount of money borrowed or invested, before any interest accrues. In simple interest, the principal remains constant throughout the term.
- Interest Rate
- The annual percentage charged on the principal. For simple interest, this rate is applied only to the original principal each period.
- Accrual Schedule
- A period-by-period breakdown showing how interest accumulates over time. Each row shows the interest earned that period and the running total.
- Maturity Value
- The total amount due at the end of the loan or investment term — the sum of principal plus all accumulated interest.
- Payment Frequency
- How often interest payments are made or calculated: monthly, quarterly, or annually. This affects the accrual schedule but not the total interest in simple interest.
Worked Examples
Example 1: Personal Loan
Scenario: Borrow $5,000 at 8% simple interest for 3 years.
Calculation: Interest = $5,000 × 0.08 × 3 = $1,200. Total repayment = $6,200. Monthly payment = $6,200 ÷ 36 = $172.22.
Example 2: CD Investment
Scenario: Invest $10,000 in a 1-year CD at 4.5% simple interest, paid quarterly.
Calculation: Annual interest = $10,000 × 0.045 = $450. Quarterly payment = $450 ÷ 4 = $112.50. Maturity value = $10,450.
Example 3: Simple vs. Compound
Scenario: $20,000 at 6% for 10 years.
Simple: $20,000 × 0.06 × 10 = $12,000 interest. Total = $32,000.
Compound: $20,000 × (1.06)^10 ≈ $35,817. Difference = $3,817. The gap widens dramatically over longer periods.
Simple vs. Compound Interest
| Duration | Simple ($10k @ 5%) | Compound ($10k @ 5%) | Difference |
|---|---|---|---|
| 1 year | $10,500 | $10,500 | $0 |
| 5 years | $12,500 | $12,763 | $263 |
| 10 years | $15,000 | $16,289 | $1,289 |
| 20 years | $20,000 | $26,533 | $6,533 |
| 30 years | $25,000 | $43,219 | $18,219 |
Understanding Simple Interest
What Is Simple Interest?
Simple interest is the most straightforward form of interest calculation. Unlike compound interest, which earns "interest on interest," simple interest applies only to the original principal. This means the interest amount is identical every period, creating linear (not exponential) growth. While less powerful for savers, it is more predictable and often more favorable for borrowers.
Where Simple Interest Is Used
Simple interest is common in auto loans, short-term personal loans, Treasury bills, and certain certificates of deposit. Many consumer loans advertise compound rates but actually calculate interest using a daily simple interest method on the outstanding principal. Understanding this distinction helps you estimate true borrowing costs and identify when early payments can significantly reduce total interest.
Simple Interest and Early Payoff
One significant advantage of simple interest loans is that paying early reduces total interest. Since interest accrues daily on the remaining principal, any extra payment directly reduces the base amount. On a $15,000 auto loan at 5%, paying just $50 extra per month can save hundreds in interest and shorten the loan by several months.
When Compound Interest Wins
For long-term investing, compound interest is dramatically superior. The comparison table above shows that over 30 years, compound interest on $10,000 at 5% produces $18,219 more than simple interest. This is why retirement accounts and index funds — which reinvest returns — are the foundation of wealth building. Simple interest is best for short-term, predictable calculations.