Compound Interest

Introduction

Compound interest is interest calculated on the initial principal plus all accumulated interest from prior periods. It accelerates growth because each period’s interest earns interest in subsequent periods. This makes compounding a powerful force for building wealth—and a costly one when applied to debt.

Key takeaways

• Compound interest = interest on principal + previously earned interest (“interest on interest”).
• More frequent compounding and longer time horizons amplify growth.
• The Rule of 72 (72 ÷ annual interest rate) estimates how long it takes for money to double.
• Compound interest can work for savers and investors, but works against borrowers with high-interest debt.

What is compound interest?

Compound interest adds accrued interest to the principal at regular intervals (annual, semi-annual, quarterly, monthly, daily, or continuously). Once added, that interest becomes part of the principal and begins earning interest itself in the next period.

How it’s calculated

The standard compound interest formulas:

Interest earned = P * [(1 + i)^n – 1]
or
Future value = P * (1 + i)^n

Where:
* P = principal (initial amount)
* i = interest rate per period
* n = number of compounding periods

Example:
A $10,000 loan at 5% compounded annually for 3 years:
Interest = $10,000 * [(1 + 0.05)^3 – 1] = $1,576.25

Rule of 72

Approximate doubling time = 72 ÷ annual interest rate (percent).
Example: At 4% annual return, money doubles in about 18 years (72 ÷ 4 = 18).

Compounding frequency

More frequent compounding increases the effective return for savers and the effective cost for borrowers. Common frequencies:
* Annual, semi-annual, quarterly, monthly, daily, continuous.

Practical note: continuous compounding yields only a small additional amount over daily compounding for typical consumer timelines.

Illustrative comparisons

• A $100,000 deposit at 5% simple interest for 10 years earns $50,000 in interest.
• The same deposit at 5% compounded monthly grows to roughly $164,700 (about $64,700 in interest).

Starting early vs. starting late (concept)

Small, consistent contributions started early can outperform larger contributions started later because of compounding over a longer period. For example:
* Start at age 20: $100/month at 4% compounded monthly until age 65 → final amount ~ $151,550 (total principal ≈ $54,100).
* Start at age 50: $5,000 initial plus $500/month at 4% compounded monthly for 15 years → final amount ~ $132,147 (total principal ≈ $95,000).

Pros and cons

Pros:
* Powerful growth for long-term savings and investments.
* Helps offset inflation and preserve purchasing power.
* Can reduce total interest paid if used to accelerate loan repayments.

Cons:
* Works against borrowers who make only minimum payments on high-interest debt.
* Interest earnings are typically taxable unless held in a tax-advantaged account.
* More complex to calculate than simple interest—tools are helpful.

Compound interest in investing

Common ways investors use compounding:
* Dividend reinvestment plans (DRIPs) automatically use dividends to buy more shares, increasing future returns.
* Zero-coupon bonds are bought at a discount and grow to face value without periodic interest payments—effectively compounding until maturity.

Calculating compound interest: tools and methods

Options:
* Formula: Use the compound interest formula directly.
* Spreadsheet (e.g., Excel):
– Iterative multiplication (year-by-year balances).
– Single-cell formula: =(P(1+i)^n)-P (or to get future value: =P(1+i)^n).
– Custom function (if desired) to reuse the calculation.
* Online calculators: many free calculators let you input principal, rate, compounding frequency, and regular contributions.

How to know if interest is compounded

For loans, lenders are required to disclose whether interest is simple or compounded and the total interest to be repaid. Check loan documents or ask the lender for the compounding frequency and effective annual rate (EAR).

Frequently asked questions

Q: What’s the simplest definition of compound interest?
A: Earning interest on both your original amount and the interest that amount has already earned.

Q: Who benefits from compound interest?
A: Savers and long-term investors benefit most. Lenders and credit card companies benefit when compounding increases the amount borrowers owe.

Bottom line

Compound interest is a fundamental force in personal finance. When used for saving and investing—especially over long time horizons and with frequent compounding—it can significantly accelerate wealth accumulation. Conversely, compounding can make high-interest debt much harder to repay. Start early, be consistent, and pay attention to compounding frequency when choosing accounts or loans.