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The key factors are:
* Principal (P): Your starting amount of money.
* Annual Interest Rate (r): The percentage your money grows each year (expressed as a decimal, e.g., 5% is 0.05).
* Number of Times Compounded Per Year (n): How often the interest is calculated and added to the principal within a year (e.g., annually n=1, semi-annually n=2, quarterly n=4, monthly n=12).
* Time (t): The number of years your money is invested or borrowed.

• Compound Interest: This is where interest earns interest. After each period, the interest earned is added to the principal, and the next period's interest is calculated on this new, larger amount. This is how most real-world investments work, and it's incredibly powerful over time.
  • Formula for Future Value: $FV = P (1 + r)^t$
    • $FV$ = Future Value
    • $P$ = Principal
    • $r$ = Annual interest rate (as a decimal)
    • $t$ = Number of compounding periods (usually years, but can be months/quarters if rate adjusted)

An annuity is a fixed series of payments or receipts over a specified period. When these payments occur at the end of each period, it's called an ordinary annuity. If they happen at the beginning, it's an annuity due. We'll focus on ordinary annuities for now, as they're more common in many applications like loan repayments or regular savings.

The future value (FV) tells you how much a series of regular payments will be worth at a specific point in the future, assuming a certain interest rate. Imagine saving the same amount every month; FVA calculates your total savings plus all the interest earned on those savings.