How to Calculate Compound Interest Step by Step

The Compound Interest Formula

The standard formula for compound interest is:

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

Where:

• A = final amount (principal + interest)
• P = initial principal (starting amount)
• r = annual interest rate (as a decimal — 7% = 0.07)
• n = number of compounding periods per year
• t = time in years

The compound interest earned is simply A − P.

Step-by-Step Example 1: Lump Sum

Problem: $5,000 invested at 6% compounded monthly for 10 years.

Step 1: Identify variables

• P = $5,000, r = 0.06, n = 12, t = 10

Step 2: Plug into formula

• A = 5000 × (1 + 0.06/12)^(12 × 10)
• A = 5000 × (1.005)^120

Step 3: Calculate the exponent

• (1.005)^120 = 1.8194

Step 4: Multiply

• A = 5000 × 1.8194 = $9,097
• Interest earned: $9,097 − $5,000 = $4,097

Step-by-Step Example 2: With Monthly Contributions

Problem: $1,000 starting balance + $200/month at 7% compounded monthly for 20 years.

Extended formula: A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]

Step 1: Calculate the lump-sum growth

• 1000 × (1 + 0.07/12)^(240) = 1000 × 4.0387 = $4,039

Step 2: Calculate the contribution growth

• 200 × [((1.00583)^240 − 1) / 0.00583]
• 200 × [(4.0387 − 1) / 0.00583]
• 200 × 521.0 = $104,200

Step 3: Add them together

• A = $4,039 + $104,200 = $108,239
• Total contributed: $1,000 + ($200 × 240) = $49,000
• Interest earned: $108,239 − $49,000 = $59,239

Common Compounding Frequencies

Frequency	n value	Used by
Daily	365	Savings accounts, CDs
Monthly	12	Investment accounts, mutual funds
Quarterly	4	Some bonds and bank accounts
Semi-annually	2	Government bonds
Annually	1	Fixed deposits, simple projections

Skip the Manual Math

While understanding the formula is valuable, you don’t need to calculate manually. Use our free compound interest calculator for instant results with charts, year-by-year breakdowns, and the ability to adjust any variable in real time.