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Interest Calculator — Simple & Compound Interest Calculator

Calculate simple and compound interest on your investments and loans

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Interest Calculator: Simple and Compound Interest Calculations

Current Interest Rate Landscape

The global interest rate environment in 2026 presents both opportunities and challenges for savers and borrowers. Central banks have navigated a complex path from the near-zero rates of 2020-2021 through aggressive tightening cycles to the current moderate levels.

| Central Bank | Current Rate | Direction | Last Change | |-------------|-------------|-----------|-------------| | Federal Reserve | 3.50-3.75% | Hold | January 2026 | | Bank of England | 3.75% | Hold | February 2026 | | European Central Bank | 2.75% | Cut | December 2025 | | Bank of Japan | 0.50% | Raise | January 2026 | | Reserve Bank of Australia | 4.10% | Hold | December 2025 |

Sources: Federal Reserve, Bank of England, Trading Economics

These rates directly influence savings account yields, mortgage costs, credit card APRs and investment returns. Understanding how interest is calculated enables more informed financial decisions.

Contents

Calculator Usage Guide

The Principal Amount field accepts the initial sum to be invested or borrowed. This value serves as the foundation for all interest calculations.

The Annual Interest Rate is entered as a percentage. For current savings accounts, rates between 4% and 5% are typical in the US and UK markets. Credit card rates commonly range from 18% to 25%.

Compounding Frequency is selected from the dropdown: Annual (1), Semi-annual (2), Quarterly (4), Monthly (12), or Daily (365). Most savings accounts compound daily; most loans compound monthly.

The Time Period is specified in years. Decimal values may be entered for partial years (e.g., 2.5 for two and a half years).

Calculation Type allows selection between Compound (standard for most modern financial products) and Simple (primarily for comparison or certain specific loan types).

Results displayed upon calculation include:

  • Final amount (principal plus accumulated interest)
  • Total interest earned or paid
  • Simple versus compound comparison
  • Effective annual rate (APY)
  • Estimated time to double the principal
  • Year-by-year breakdown of growth

Simple Versus Compound Interest

Interest represents the cost of borrowing money or the reward for saving it. Two fundamental calculation methods exist, and understanding the distinction between them affects financial outcomes significantly.

Simple Interest

Simple interest is calculated solely on the original principal. The formula is:

Interest = Principal × Rate × Time

Consider £10,000 at 5% simple interest for 5 years: Interest = £10,000 × 0.05 × 5 = £2,500 Final amount = £12,500

Simple interest produces linear growth. Each year adds exactly the same amount: £500 in this example.

Compound Interest

Compound interest is calculated on the principal plus all previously accumulated interest. The formula is:

Amount = Principal × (1 + Rate/n)^(n×Time)

The same £10,000 at 5% compounded annually for 5 years: Amount = £10,000 × (1.05)^5 = £12,762.82 Interest = £2,762.82

The £262.82 difference represents "interest on interest"—the defining characteristic of compound growth.

The Compounding Frequency Effect

More frequent compounding produces marginally higher returns because interest begins earning interest sooner. For £10,000 at 5% for 5 years:

| Frequency | Final Amount | Interest Earned | |-----------|-------------|-----------------| | Annual | £12,762.82 | £2,762.82 | | Quarterly | £12,820.37 | £2,820.37 | | Monthly | £12,833.59 | £2,833.59 | | Daily | £12,840.03 | £2,840.03 |

The difference between annual and daily compounding amounts to £77.21 over five years—meaningful but less dramatic than often assumed.

Current Data: What Rates Mean for Your Money

UK Savings Scenario (February 2026)

With the Bank of England base rate at 3.75%, competitive easy-access savings accounts offer approximately 4.0-4.5% AER.

Calculation: £20,000 in a 4.25% AER Account

Amount = £20,000 × (1.0425)^3 Amount = £22,646.70 Interest earned = £2,646.70

However, UK inflation stands at 3.4%. The real return is therefore:

Real return ≈ 4.25% - 3.4% = 0.85%

In purchasing power terms, the £22,646.70 after three years is worth approximately £20,520 in today's money. Whilst nominal growth occurs, real wealth accumulation is modest.

US Credit Card Debt Scenario

Average US credit card interest rates currently exceed 20% APR. The Federal Reserve reports the average rate at 21.76% as of Q4 2025.

Calculation: $5,000 Credit Card Balance at 21.76% APR

If making only minimum payments (typically 2% of balance or $25, whichever is higher), the repayment trajectory is concerning:

After 1 year (minimum payments only): Balance ≈ $4,800 (slow principal reduction) Interest paid ≈ $1,050

After 5 years (minimum payments only): Balance ≈ $3,200 Total interest paid ≈ $4,100

The original $5,000 purchase costs over $9,000 with minimum payments. This demonstrates compound interest working against the borrower.

Nigerian Treasury Bill Investment

The Central Bank of Nigeria projects inflation at 12.94% for 2026, whilst treasury bill yields offer approximately 20%.

Calculation: ₦10,000,000 in 1-Year Treasury Bills at 20%

Interest = ₦10,000,000 × 0.20 × 1 Interest = ₦2,000,000 Total = ₦12,000,000

Nominal return: 20% Real return (after inflation): 20% - 12.94% = 7.06%

This demonstrates why emerging market yields appear high but must be evaluated against local inflation rates.

Multi-Country Interest Comparison

Interest rates and their effects vary substantially across economies. The following comparison illustrates how identical savings behaviour produces different outcomes.

Scenario: £10,000 Equivalent Saved for 10 Years

| Country | Savings Rate | Inflation | Real Rate | Final Value (Nominal) | Final Value (Real) | |---------|-------------|-----------|-----------|----------------------|-------------------| | United Kingdom | 4.25% | 3.4% | 0.85% | £15,162 | £10,883 | | United States | 4.50% | 2.9% | 1.60% | $15,530 | $12,172 | | Japan | 0.30% | 2.8% | -2.50% | ¥1,030,451 | ¥760,000 | | Nigeria | 20.0% | 12.9% | 7.10% | ₦61,917,000 | ₦29,900,000 | | Australia | 4.80% | 3.6% | 1.20% | A$15,999 | A$11,500 |

Sources: World Bank, Trading Economics, Central bank publications

Key observations:

Japan's near-zero interest rates combined with positive inflation produce negative real returns. Savers lose purchasing power despite positive nominal interest.

Nigeria's high nominal rates deliver attractive real returns, though currency volatility and accessibility present additional considerations for international comparisons.

The UK and US offer similar real returns despite different nominal rates, as inflation differences approximately offset interest rate differences.

Global Household Savings Behaviour

According to World Bank data, gross national savings rates vary considerably:

  • Singapore: 52% of GDP
  • China: 44% of GDP
  • Germany: 28% of GDP
  • Nigeria: 21% of GDP
  • United States: 18% of GDP
  • United Kingdom: 14% of GDP

Higher-saving nations benefit more from compound interest effects at the macroeconomic level, contributing to capital formation and investment capacity.

Cryptocurrency Yield Comparison

Decentralised finance (DeFi) and cryptocurrency staking offer alternative yield opportunities that merit comparison with traditional interest products.

Ethereum Staking

Ethereum proof-of-stake validators currently earn approximately 3.5-5.5% APY. This yield is denominated in ETH rather than fiat currency.

Calculation: 10 ETH Staked at 4.5% APY for 3 Years

Amount = 10 × (1.045)^3 Amount = 11.41 ETH ETH earned = 1.41 ETH

The dollar value depends entirely on ETH price movements. If ETH appreciates, total returns exceed the staking yield. If ETH depreciates, losses may occur despite positive staking returns.

Stablecoin Lending Yields

DeFi protocols offering stablecoin yields (USDC, USDT) currently advertise rates between 3% and 8% APY. These rates compete with traditional savings accounts but carry smart contract risks, regulatory uncertainty and counterparty risks absent from bank deposits.

Comparison: $10,000 for 1 Year

| Product | APY | Final Value | Risk Profile | |---------|-----|-------------|--------------| | UK Savings Account | 4.25% | $10,425 | FSCS protected (£85k) | | US Savings Account | 4.50% | $10,450 | FDIC insured ($250k) | | Stablecoin DeFi | 6.00% | $10,600 | No deposit protection | | ETH Staking | 4.50% | Variable | Price + smart contract risk |

The additional yield from DeFi products must be evaluated against the absence of deposit insurance and the technical risks involved.

Bitcoin: No Traditional Interest

Bitcoin does not generate interest through holding. Yield-generating Bitcoin products (wrapped BTC in DeFi, centralised lending) introduce counterparty and smart contract risks. Several high-profile failures (Celsius, BlockFi, Voyager) demonstrated these risks materially in 2022.

Manual Calculation Methods

Simple Interest

Interest = P × r × t

Where P = principal, r = annual rate (decimal), t = time in years

Example: £8,000 at 3.5% for 4 years Interest = 8,000 × 0.035 × 4 = £1,120 Final amount = £9,120

Compound Interest (Annual)

A = P × (1 + r)^t

Example: £8,000 at 3.5% for 4 years A = 8,000 × (1.035)^4 = £9,181.43 Interest = £1,181.43

Compound Interest (Sub-Annual Compounding)

A = P × (1 + r/n)^(n×t)

Where n = compounding frequency per year

Example: £8,000 at 3.5% for 4 years, monthly compounding A = 8,000 × (1 + 0.035/12)^(12×4) A = 8,000 × (1.002917)^48 A = 8,000 × 1.1503 A = £9,202.40

Effective Annual Rate (APY)

APY = (1 + r/n)^n - 1

Example: 3.5% APR compounded monthly APY = (1 + 0.035/12)^12 - 1 APY = 1.0356 - 1 = 3.56%

Rule of 72 (Doubling Time)

Years to double ≈ 72 / Interest rate

At 4%: 72/4 = 18 years At 6%: 72/6 = 12 years At 8%: 72/8 = 9 years At 12%: 72/12 = 6 years

This mental calculation enables rapid estimation without detailed computation.

Converting Between APR and APY

APY from APR: APY = (1 + APR/n)^n - 1 APR from APY: APR = n × [(1 + APY)^(1/n) - 1]

Limitations and Considerations

Inflation Erosion

Interest calculations produce nominal returns. Real returns require inflation adjustment. A 5% nominal return with 3% inflation yields approximately 2% real return. Over extended periods, inflation's cumulative effect is substantial; 3% annual inflation reduces purchasing power by approximately 50% over 24 years.

Tax Impact

Interest income is typically taxable. In the UK, the Personal Savings Allowance permits £1,000 (basic rate) or £500 (higher rate) of interest tax-free. Above these thresholds, interest is taxed at marginal rates. A 4% gross return at 40% tax becomes 2.4% net.

Fee Considerations

Investment products carrying fees reduce effective returns. A 1% annual fee on a 5% gross return leaves 4% net—equivalent to 20% of returns consumed by fees. Over 30 years, this compounds to substantial impact.

Variable Rate Uncertainty

This calculator assumes fixed rates. Savings account rates, adjustable mortgages and many financial products have variable rates. Projections should be recalculated when rates change.

Compound Interest on Debt

The same mathematics that grows savings erodes borrowers' positions. Credit card balances at 20%+ APR compound against the debtor. Minimum payments are structured to maximise interest collection over extended periods.

Currency Risk

International interest rate comparisons must account for currency movements. High-yield emerging market deposits may lose value if the local currency depreciates against the investor's home currency.

How This Calculator Works

Simple Interest Calculation:

simpleInterest = P × r × t simpleAmount = P + simpleInterest

Compound Interest Calculation:

compoundAmount = P × (1 + r/n)^(n×t) compoundInterest = compoundAmount - P

Effective Annual Rate:

effectiveRate = ((compoundAmount / P)^(1/t) - 1) × 100

Time to Double (Rule of 72 approximation):

doubleTime = ln(2) / (n × ln(1 + r/n))

Year-by-Year Breakdown:

For each year from 1 to the specified period:

  • Simple: P × (1 + r × year)
  • Compound: P × (1 + r/n)^(n × year)
  • Difference: compound - simple

All calculations are processed locally in the browser.

Sources

FAQs

What distinguishes APR from APY?

APR (Annual Percentage Rate) is the stated nominal rate without compounding adjustments. APY (Annual Percentage Yield) reflects the effective rate after compounding. A 5% APR compounded monthly produces approximately 5.12% APY. Savings comparisons should employ APY; loan comparisons typically use APR with matching compounding frequencies.

How does compounding frequency affect returns?

More frequent compounding produces marginally higher returns because interest begins earning interest sooner. However, the effect is modest. The difference between annual and daily compounding at 5% amounts to approximately 0.13% APY—£13 per £10,000 annually. Time and rate matter far more than compounding frequency.

Which produces more interest: simple or compound?

Compound interest always produces more interest than simple interest over multiple periods (assuming positive rates). The gap widens as time extends. For a 10-year investment at 5%, compound interest yields 17% more than simple interest.

How should inflation be incorporated into interest calculations?

Real return ≈ Nominal return - Inflation rate. For precise calculation: Real return = (1 + nominal) / (1 + inflation) - 1. A 5% nominal return with 3% inflation produces approximately 1.94% real return.

What is the Rule of 72?

A mental calculation tool: divide 72 by the interest rate to estimate years required to double an investment. At 6%, money doubles in approximately 12 years. The rule provides quick estimates without calculation.

How do cryptocurrency yields compare to traditional interest?

Cryptocurrency staking and DeFi yields (typically 3-12% for major assets) may appear competitive but carry risks absent from traditional savings: smart contract vulnerabilities, regulatory uncertainty, token price volatility and lack of deposit insurance. Returns are denominated in the staked asset, not fiat currency.

Why do emerging markets offer higher interest rates?

Higher interest rates compensate for higher inflation, currency risk and default risk. Nigeria's 20% treasury bill yields must be evaluated against 13% inflation and naira volatility. The real return, whilst still attractive, is significantly lower than the nominal rate suggests.

How do taxes affect interest earnings?

Interest is typically taxable as income. After-tax return = Gross return × (1 - tax rate). A 4% return taxed at 40% becomes 2.4% net. Tax-advantaged accounts (ISAs in the UK, Roth IRAs in the US) allow interest to compound without annual tax drag.

Is daily compounding significantly better than monthly?

Marginally. At 5% APR, daily compounding produces 5.127% APY versus monthly compounding at 5.116% APY—a difference of 0.011% or £1.10 per £10,000 annually. The difference compounds over decades but is rarely the deciding factor between financial products.

How does compound interest apply to mortgages?

Mortgages compound interest on the outstanding balance, typically monthly. However, unlike savings accounts where balances grow, mortgage balances decrease as principal payments reduce the outstanding amount. The effect remains compound—interest is calculated on the current balance including any unpaid interest—but the declining balance trajectory differs from savings growth.

What happens if I withdraw interest instead of reinvesting?

Withdrawing interest converts compound interest behaviour to effective simple interest. The principal remains constant, earning the same absolute amount each period. For income-focused investors, this may be appropriate; for growth-focused investors, reinvestment maximises long-term accumulation.