Simple interest is calculated only on the initial principal and does not compound over time. The accumulation function describes how an investment or loan grows under simple interest.
1. Simple Interest Accumulation Function
The accumulation function for simple interest is:
A(t) = P (1 + rt)
- A(t) = Accumulated amount at time t
- P = Principal (initial investment)
- r = Annual interest rate (decimal)
- t = Number of years
2. Example of Simple Interest Calculation
Scenario: You invest $10,000 at an annual interest rate of 5% for 10 years.
A(10) = 10,000 × (1 + 0.05 × 10)
A(10) = 10,000 × (1 + 0.5)
A(10) = 10,000 × 1.5
A(10) = $15,000
3. Comparison with Compound Interest
For the same investment ($10,000 at 5% for 10 years), the accumulated amounts differ:
- Simple Interest: $15,000
- Annual Compounding (5%): $16,288.95
- Monthly Compounding (5%): $16,470.09
- Continuous Compounding (5%): $16,487.21