Charles Edison is a Certified Financial Planner with expertise in long-term wealth accumulation and investment growth modeling, ensuring precise calculation of compounded returns.
Use the authoritative **Compound Interest Calculator** to model the growth of your investments where interest is reinvested. Enter any three variables—Future Value, Annual Rate, Time in Years, or Principal Amount—to solve for the remaining unknown variable.
Compound Interest Calculator
Compound Interest Formula
Core Compound Interest Relationship (Single Lump Sum, Annual Compounding):
$$ FV = P \times (1 + r)^n $$
The four solution formulas:
P (Principal, Q) $= \text{FV} / (1 + r)^n$
FV (F) $= \text{P} \times (1 + r)^n$
r (Rate, P) $= [(FV / P)^{1/n} – 1] \times 100$
n (Time, V) $= \frac{\ln(FV / P)}{\ln(1 + r)}$
Formula Source: InvestopediaFormula Variables
- F ($\mathbf{FV}$ – Future Value): The final amount of the investment after compounding.
- P ($\mathbf{r}$ – Annual Rate): The annual interest rate (as a decimal in formulas).
- V ($\mathbf{n}$ – Time): The number of compounding periods (assumed years for annual compounding).
- Q ($\mathbf{P}$ – Principal): The initial, single lump sum amount invested or borrowed.
Related Calculators
- Future Value Calculator
- Simple Interest Calculator
- Time to Double (Rule of 72) Calculator
- Present Value Calculator
What is Compound Interest?
Compound interest is the interest on a loan or investment calculated based on both the initial principal and the accumulated interest from previous periods. It is often described as “interest on interest” and is the driving force behind long-term wealth creation. Unlike simple interest, which grows linearly, compound interest exhibits exponential growth, meaning the amount of money earned accelerates over time.
The calculation relies heavily on three factors: the rate, the time period, and the frequency of compounding. While this calculator assumes annual compounding for simplicity, most real-world instruments (like bank accounts) compound more frequently (quarterly, monthly, or daily). Even with annual compounding, the effect of reinvesting earnings is powerful, making compound interest the single most important concept in finance.
How to Calculate Required Principal (Example)
Let’s find the Principal (Q) needed to reach a Future Value (F) of \$50,000 in 15 years (V) at a 7\% annual rate (P).
- Step 1: Determine Known Variables
$FV = \$50,000$. $r = 7\%$ (0.07). $n = 15$ years.
- Step 2: Calculate the Discount Factor $(1 + r)^n$
Discount Factor $= (1 + 0.07)^{15} \approx 2.75903$.
- Step 3: Apply the Principal Formula ($\mathbf{P = FV / (1 + r)^n}$)
Principal ($P$) = $\$50,000 / 2.75903$.
- Step 4: Determine the Required Principal
The calculation yields a required Principal (Q) of approximately **\$18,122.84**.
Frequently Asked Questions (FAQ)
The Compound Interest Calculator applies interest to the running total (principal + accumulated interest), whereas the Simple Interest Calculator only applies interest to the original principal amount, resulting in significantly different totals over long time periods.
What is the “Rule of 72”?The Rule of 72 is a quick way to estimate the number of years it takes for an investment to double in value. You simply divide 72 by the annual rate of return (e.g., at 6%, it takes $72 / 6 = 12$ years to double).
Does compounding frequency matter?Yes, the more frequently interest is compounded (e.g., monthly vs. annually), the higher the effective annual rate (EAR) will be. This calculator assumes annual compounding for simplicity, but more frequent compounding would yield a slightly higher Future Value (F).
If I solve for a negative rate, what does that mean?A negative rate (P) result means your Future Value (F) is less than your Principal (Q). This indicates that the investment lost money over the period (e.g., due to fees or inflation-adjusted losses).