Interest Calculator

Interest Formulas

Simple: I = P × r × t
Compound: A = P(1 + r/n)^(nt)

Quick Reference

Simple Interest
I = P × r × t
Compound Interest
A = P(1 + r/n)^(nt)
Rule of 72
Years to double = 72 / rate%

Understanding Interest

Simple vs. Compound Interest

Interest is the cost of borrowing money or the reward for saving. Understanding the difference between simple and compound interest is crucial for making informed financial decisions about loans, investments, and savings.

Simple Interest

Calculated only on the original principal. The interest amount stays constant each period.

I = P × r × t

P = Principal, r = rate, t = time

Compound Interest

Calculated on principal plus accumulated interest. Interest earns interest, leading to exponential growth.

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

n = compounds per year

Example Comparison

$10,000 invested at 5% annual interest for 10 years:

YearSimple InterestCompound (Monthly)Difference
1$10,500$10,512+$12
5$12,500$12,834+$334
10$15,000$16,470+$1,470
20$20,000$27,126+$7,126

Compounding Frequency Matters

More frequent compounding leads to higher returns. The same 5% rate produces different results based on compounding frequency:

FrequencyTimes/Year$10,000 after 1 yearEffective Rate
Annual1$10,500.005.000%
Semi-annual2$10,506.255.063%
Quarterly4$10,509.455.095%
Monthly12$10,511.625.116%
Daily365$10,512.675.127%

The Rule of 72

Quick Mental Math

To estimate how long it takes to double your money with compound interest:

Years to Double = 72 / Interest Rate
Examples: At 6% = 12 years, At 8% = 9 years, At 12% = 6 years

Where Each Type is Used

Simple Interest

  • Auto loans
  • Short-term personal loans
  • Some bonds
  • Interest-only mortgages

Compound Interest

  • Savings accounts
  • Credit cards
  • Mortgages
  • Investment accounts

Key Insight

Compound interest works in your favor for savings and investments, but against you for debt like credit cards. Paying off high-interest debt quickly is crucial because the same compounding that grows your savings also grows your debt.

Frequently Asked Questions

What is the difference between simple and compound interest?

Simple interest is calculated only on the original principal (Interest = Principal x Rate x Time). Compound interest is calculated on the principal plus accumulated interest, leading to exponential growth. Compound interest earns 'interest on interest,' making it much more powerful for long-term investments.

How do I calculate compound interest?

Use the formula: A = P(1 + r/n)^(nt), where A is the final amount, P is principal, r is annual interest rate, n is compounding frequency per year, and t is time in years. For example, $10,000 at 5% compounded monthly for 10 years: A = $10,000(1 + 0.05/12)^(12x10) = $16,470.

How does compounding frequency affect my returns?

More frequent compounding yields slightly higher returns. Annual compounding at 5% gives you exactly 5% return, while monthly compounding gives 5.12% effective rate, and daily gives 5.13%. The difference grows with higher rates and longer time periods, but is relatively small for typical savings rates.

What is the Rule of 72?

The Rule of 72 is a quick way to estimate how long it takes to double your money with compound interest. Divide 72 by your annual interest rate. At 6% interest, money doubles in about 12 years (72/6). At 8%, it doubles in 9 years. This approximation works best for rates between 6-10%.