Compound Interest Investment Calculator
Compound Interest Calculator
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The compound interest calculator shows you exactly how money grows when interest is reinvested. Unlike simple interest, compound interest earns returns on both the original amount and on past interest. The longer the time period and the more frequent the compounding, the greater the growth.
The Compound Interest Formula
A = P(1 + r/n)^(nt)
A = final amount. P = principal (starting amount). r = annual interest rate (decimal). n = times interest compounds per year. t = years.
Variable Explanations
| Variable | Meaning | Example |
|---|---|---|
| P | Principal (starting amount) | $10,000 |
| r | Annual interest rate as a decimal | 0.07 for 7% |
| n | Compounding frequency per year | 12 for monthly |
| t | Time in years | 20 |
| A | Final amount after t years | Result of formula |
Monthly vs. Annual Compounding
| Compounding Frequency | $10,000 at 7% over 20 years |
|---|---|
| Annually (n=1) | $38,697 |
| Quarterly (n=4) | $39,960 |
| Monthly (n=12) | $40,170 |
| Daily (n=365) | $40,255 |
Worked Examples
Example 1 (Savings): You invest $5,000 at 6% per year, compounding monthly, for 10 years. A = 5,000 x (1 + 0.06/12)^(12x10) = 5,000 x (1.005)^120 = 5,000 x 1.8194 = $9,097. Example 2 (Debt): You carry $3,000 on a credit card at 20% APR compounding daily. After 3 years of no payments, the balance grows to $3,000 x (1 + 0.20/365)^(365x3) = $5,466. Example 3 (Retirement): $500/month invested at 8% over 30 years grows to approximately $680,000 using compound growth.
The Rule of 72
To quickly estimate how long it takes to double money, divide 72 by the annual interest rate. At 6%, money doubles in 72/6 = 12 years. At 9%, it doubles in 8 years. This rule works for interest rates between 6% and 10% and gives a close approximation.
Doubling Time (years) = 72 / Annual Interest Rate (%)
Example: 72 / 8% = 9 years to double at 8% annual return.
Frequently Asked Questions
What is the difference between simple interest and compound interest?⌄
Simple interest calculates returns only on the original principal. Compound interest calculates returns on the principal plus all previously earned interest. Over long periods, compound interest produces significantly more growth. On a $10,000 investment at 7% for 20 years, simple interest gives $14,000 in interest. Compound interest (monthly) gives $30,170.
How often does interest compound?⌄
It depends on the account or investment. Savings accounts typically compound daily or monthly. Bonds usually compound semi-annually. Most investment returns are quoted annually. The more frequently interest compounds, the more you earn, but the difference between daily and monthly compounding is small.
What is the best interest rate for compound interest?⌄
Higher is always better when saving, and lower is always better when borrowing. For savings, look for high-yield accounts offering 4-5% in current markets. For investments, historical stock market returns average 7-10% annually before inflation.
Does compound interest work against you with debt?⌄
Yes. Compound interest is powerful for growth but damaging for debt. Credit card balances at 20-24% APR compounding daily can more than double in 3-4 years with no payments. Pay off high-interest debt before investing.
How much will $1,000 grow to in 10 years at 5%?⌄
$1,000 at 5% compounded annually for 10 years grows to $1,629. Compounded monthly, it grows to $1,647. Use this calculator with your exact values to get a precise projection.