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Compound Growth

Compound Interest

Growth that results from earning interest on both the principal and previously earned interest.

01 / Formula

Formula

A = P(1 + r/n)^(nt)

02 / Variables

Variables

A: Final amount
P: Principal (starting amount)
r: Annual rate (as decimal)
n: Compounding periods per year
t: Time in years

03 / Worked Example

Worked Example

Scenario: $1,000 at 5% annual interest compounded monthly for 10 years becomes approximately $1,644.

Steps:

Convert 5% to decimal: 0.05
Divide by 12: 0.05/12 = 0.00417
Calculate (1 + 0.00417) = 1.00417
Raise to power 120 (12 × 10 months): 1.00417^120 = 1.6453
Multiply by principal: $1,000 × 1.6453 = $1,645.30

04 / When to Use

When to Use This Formula

Calculate savings growth
Estimate investment returns
Compare compounding frequencies

05 / Limitations

Limitations & Assumptions

Assumes no additional deposits or withdrawals
Ignores inflation and taxes
Compounding frequency affects the outcome significantly

06 / Questions

Common Questions

What compounding frequency should I use?

Check your account or investment terms. Common frequencies: daily (365), monthly (12), quarterly (4), annually (1).

Does more frequent compounding always result in more money?

Yes, but the difference decreases at high frequencies. Monthly vs. daily makes more difference than daily vs. continuously.

More on this topic

Compound growth and regular investing

Reference note: This is an educational mathematical reference. The formula's applicability depends on assumptions, market conditions, and use case. Always verify results independently and consult domain experts for decisions.