Key Details of a Compound Interest Calculator

1. Principal Amount (P):
   The initial sum of money invested or borrowed.

2. Interest Rate (r):
   The annual nominal interest rate, expressed as a decimal (e.g., 5% = 0.05).

3. Compounding Frequency (n):
   How often interest is applied to the principal within a year. Common compounding intervals are:

   • Annually (1 time per year)
   • Semiannually (2 times per year)
   • Quarterly (4 times per year)
   • Monthly (12 times per year)
   • Daily (365 times per year)

4. Time (t):
   The total duration for which the money is invested or borrowed, typically in years.

5. Formula Used:
   The compound interest formula is:

   A=P×(1+rn)n×tA = P \times \left(1 + \frac{r}{n}\right)^{n \times t}A=P×(1+nr​)n×t

   Where:

   • $A$ = Future Value (Total amount after interest)
   • $P$ = Principal
   • $r$ = Annual Interest Rate (decimal)
   • $n$ = Number of compounding periods per year
   • $t$ = Time in years

6. Interest Earned (I):
   To find the interest earned, subtract the principal from the future value:

   $$I=A-P$$

7. Adjustments for Additional Contributions:
   Some calculators account for periodic additional contributions (deposits or payments), enabling more dynamic projections.

8. Applications:

   • Savings growth estimation: Helps plan long-term savings.
   • Loan repayment planning: Shows total interest paid on a loan.
   • Investment performance tracking: Forecasts the return on investments.

9. Key Assumptions:

   • Interest rates remain constant.
   • Compounding frequency is consistent.
   • No withdrawals or interruptions in the calculation period unless specified.

This tool is invaluable for financial planning, enabling users to visualize how compounding can amplify savings or debt over time.