Simple and Compound Interest Guide
Quick Answer
Simple Interest: SI = P × R × T
Where P = principal, R = annual rate as decimal, T = time in years.
Compound Interest: A = P × (1 + r/n)^(n × t)
Where n = compounding frequency per year.
Example: 10,000 at 8% for 5 years
- Simple Interest: SI = 10,000 × 0.08 × 5 = 4,000. Total = 14,000.
- Compound (annual): A = 10,000 × (1.08)^5 = 14,693. Interest = 4,693.
Interest is money paid for the use of borrowed money, or earned on saved money. Whether you are taking a personal loan, paying a mortgage or investing in a savings account, knowing how interest works is essential. Use the Retirement Calculator and Mortgage Calculator on CalConvs which both incorporate compound interest calculations.
Simple Interest: When It Applies
SI = P × R × T
- Example 1: Borrow 5,000 at 10% per year for 3 years. SI = 5,000 × 0.10 × 3 = 1,500. Total repayment = 6,500.
- Example 2: Invest 2,000 in a simple interest bond at 6% for 2 years. SI = 2,000 × 0.06 × 2 = 240. Total = 2,240.
Simple interest is used for: car loans in some countries, short-term personal loans, government savings certificates (e.g. Pakistan NSS, India KVP) and some fixed deposit products.
Compound Interest: When It Applies
A = P × (1 + r/n)^(n × t)
Example: 10,000 at 7% for 10 years, compounded monthly (n = 12).
A = 10,000 × (1 + 0.07/12)^(12 × 10) = 10,000 × (1.005833)^120 = 10,000 × 2.0097 = 20,097.
Interest earned = 10,097.
Compound interest is used for: mortgages, credit cards, bank savings accounts, investment funds, pension funds, 401k and IRA accounts (US), ISA accounts (UK).
How Compounding Frequency Affects Growth
$10,000 invested at 8% per year for 10 years:
| Compounding | Final Amount | Interest Earned |
|---|---|---|
| Simple interest (no compounding) | 18,000 | 8,000 |
| Annually (n = 1) | 21,589 | 11,589 |
| Quarterly (n = 4) | 22,080 | 12,080 |
| Monthly (n = 12) | 22,196 | 12,196 |
| Daily (n = 365) | 22,255 | 12,255 |
Interest Rates by Country: Context
- United States: Savings accounts 4 to 5% (2024). 30-year mortgage rates approximately 6.5 to 7%. Credit card rates 20 to 30% APR.
- United Kingdom: Savings accounts 4 to 5% (2024). Fixed mortgage rates 4.5 to 5.5%. Credit cards 20 to 30% APR.
- India: Bank FD rates 6.5 to 7.5% (2024). Home loan rates 8.5 to 9.5%. PPF at 7.1% government guaranteed.
- Pakistan: NSS products 12 to 14% (2024, varies by scheme). Bank loan rates 18 to 25%. Savings accounts 10 to 12%.
- Australia: Savings accounts 4 to 5% (2024). Home loan variable rates 6 to 7%.
Frequently Asked Questions
What is the difference between APR and interest rate?
The interest rate is the base cost of borrowing. APR (Annual Percentage Rate) includes the interest rate plus all fees and charges, expressed as an annual percentage. APR is a more accurate measure of the true annual cost of credit. Always compare loans using APR.
How do I calculate monthly interest on a loan?
For a simple interest loan: Monthly interest = Principal × (Annual rate ÷ 12). For a compound monthly loan: the payment is calculated using the amortisation formula, which the Mortgage Calculator applies automatically.
What is the difference between nominal and effective interest rate?
The nominal rate is the stated annual rate. The effective rate accounts for compounding within the year. A loan at 12% compounded monthly has an effective annual rate of (1 + 0.12/12)^12 - 1 = 12.68%.
Related Tools
- Mortgage Calculator: monthly payments using compound amortisation
- Retirement Calculator: savings growth with compound returns
- Inflation Calculator: compare interest returns against inflation
- All Finance Tools: browse all finance tools on CalConvs