🔄 Simple vs Compound Returns

Simple Returns (Linear Growth)

How Simple Interest Works:

Profit or interest calculated only on original principal, not reinvested.

Example:

• Principal: $10,000
• Interest rate: 5% annually
• Term: 5 years
• Year 1: $10,000 × 5% = $500 interest → $10,500
• Year 2: $10,000 × 5% = $500 interest → $11,000
• Year 3: $10,000 × 5% = $500 interest → $11,500
• Year 4: $10,000 × 5% = $500 interest → $12,000
• Year 5: $10,000 × 5% = $500 interest → $12,500
• Total gain: $2,500 (5 × $500)

Where Simple Interest Applies:

Rare in NZ investing. Most investments use compound returns. Simple interest might apply to certain short-term loans or specific financial products.

Compound Returns (Exponential Growth)

How Compound Interest Works:

Profit or interest reinvested, earning returns on both principal AND previous returns.

Same Example with Compounding:

• Principal: $10,000
• Interest rate: 5% annually compounded
• Term: 5 years
• Year 1: $10,000 × 1.05 = $10,500
• Year 2: $10,500 × 1.05 = $11,025
• Year 3: $11,025 × 1.05 = $11,576
• Year 4: $11,576 × 1.05 = $12,155
• Year 5: $12,155 × 1.05 = $12,763
• Total gain: $2,763

Compound vs Simple Comparison:

• Compound: $2,763 gain
• Simple: $2,500 gain
• Difference: $263 extra from compounding
• Percentage advantage: 10.5% more

The Power of Compounding Over Time:

Same $10,000 at 5% annual compound over different timeframes:

• 5 years: $12,763 (+$263 vs simple)
• 10 years: $16,289 (+$1,289 vs simple)
• 20 years: $26,533 (+$6,533 vs simple)
• 30 years: $43,219 (+$18,219 vs simple)

Key Insight:

Compounding advantage grows dramatically over time. The difference seems small initially but becomes enormous over decades. This is why starting early matters so much for retirement savings.

Where Compounding Applies in NZ:

• Term deposits: If you reinvest interest
• Shares: If you reinvest dividends
• KiwiSaver: Returns reinvested automatically
• Managed funds: Returns reinvested
• Property (indirectly): If you don't extract equity, capital gains compound

Compounding Frequency:

How often interest compounds affects total return:

• Annually: Once per year
• Quarterly: Four times per year (higher total return)
• Monthly: Twelve times per year (even higher)
• Daily: Every day (highest total return)

Example of Frequency Impact:

$10,000 at 5% for 1 year:

• Compounded annually: $10,500
• Compounded quarterly: $10,509
• Compounded monthly: $10,512
• Compounded daily: $10,513

Difference is small over one year, but matters more over longer periods and at higher rates.

📊 Annualised Returns and Comparing Investments

Annualised Returns

What Annualised Means:

Converting investment return over any time period into equivalent annual rate. Essential for comparing investments with different timeframes.

Why Annualise?

You can't directly compare:

• 6-month term deposit returning 2.5%
• 3-year managed fund returning 18%
• 10-year share portfolio returning 120%

Annualising puts them on common ground - all expressed as yearly rates.

Simple Annualisation Example:

Investment returned 15% over 3 years:

• Simple calculation: 15% ÷ 3 = 5% per year
• This is approximate, doesn't account for compounding

Proper Annualisation (Compound Annual Growth Rate - CAGR):

Example:

• Starting value: $10,000
• Ending value after 3 years: $11,500
• CAGR = [($11,500 ÷ $10,000)^(1 ÷ 3)] - 1
• CAGR = [1.15^0.333] - 1
• CAGR = 1.0477 - 1 = 0.0477 = 4.77% per year

Why CAGR Matters:

Smooths out volatility to show average annual growth rate. Accounts for compounding properly. Standard metric for comparing investment performance.

Comparing Investments

Beyond Just Returns:

Rate of return is important but not the only factor when comparing investments.

Factors to Consider:

1. Return:

• Historical average return
• Current yield or expected return
• Consistency of returns

2. Risk:

• Volatility - how much returns fluctuate
• Downside risk - maximum loss historically
• Generally: higher return = higher risk

3. Timeframe:

• How long must money be invested?
• Liquidity - can you access funds if needed?
• Early withdrawal penalties?

4. Fees:

• Management fees reduce net returns
• Transaction costs
• Example: 7% return minus 1% fee = 6% net return

5. Tax Treatment:

• PIE funds: capped tax rate (often advantageous)
• Shares: dividends taxed at marginal rate
• KiwiSaver: tax on returns but not contributions/withdrawals
• Property: no capital gains tax in NZ (except bright-line)

Risk-Return Trade-Off:

Fundamental principle: higher potential returns come with higher risk.

Note: These are historical averages - actual returns vary significantly year to year, especially for higher-risk investments.

Real vs Nominal Returns (Inflation Impact)

Nominal Return:

The stated return - what you see on your statement or bank advertises.

Real Return:

Return after adjusting for inflation - measures actual purchasing power growth.

Formula:

Why Inflation Matters:

Money grows but prices also rise. If returns don't exceed inflation, purchasing power decreases despite numerical growth.

Example:

• Investment: $10,000
• Nominal return: 5% (grows to $10,500)
• Inflation: 3%
• Real return: 5% - 3% = 2%
• Purchasing power: $10,500 in new money buys what $10,200 bought last year

The Inflation Trap:

Low-returning "safe" investments can lose purchasing power:

• Savings account: 1% return
• Inflation: 3%
• Real return: -2% (losing purchasing power despite growing balance)

Historical NZ Inflation:

New Zealand inflation has varied significantly:

• Recent years: 1-7% (varied significantly due to COVID impacts)
• Reserve Bank target: 1-3% range
• Long-term average: ~2-2.5%

Investment Implications:

To preserve and grow purchasing power over long term, need investments with returns exceeding inflation by meaningful margin. Term deposits at 5% with 3% inflation = 2% real return. Shares averaging 9% with 3% inflation = 6% real return.

💡 NZ Scenario and Common Misunderstandings

NZ Scenario: Sarah, 35, Comparing Investment Options

Background: Sarah has $50,000 to invest. Considering her options.

Option 1: 1-Year Term Deposit

• Amount: $50,000
• Interest rate: 5.5% per annum
• Term: 1 year
• After 1 year: $50,000 × 1.055 = $52,750
• Gain: $2,750
• Return: 5.5%
• Risk: Essentially zero (guaranteed)
• Tax: Interest taxed at marginal rate (assume 30%) = $825
• After-tax return: $2,750 - $825 = $1,925 (3.85%)
• If inflation 3%: Real return ~0.85%

Option 2: Diversified NZ/Global Share ETF (Simplicity Growth Fund or Similar)

• Amount: $50,000
• Expected long-term return: ~8% per year average
• Volatility: Returns vary significantly year to year
• Possible outcomes over 1 year:
  • Good year: +15% ($57,500, gain $7,500)
  • Average year: +8% ($54,000, gain $4,000)
  • Bad year: -10% ($45,000, loss $5,000)
• Management fee: ~0.5% annually
• Tax: PIE fund, taxed at prescribed rate (likely 17.5-28%)
• Liquidity: Can sell anytime (3-5 days to access cash)
• Risk: Moderate to high - short-term volatility

Sarah's Analysis:

1-Year Timeframe:

If Sarah needs money in 1 year (house deposit, wedding, etc.), term deposit is safer choice. Guaranteed return, no volatility risk, knows exactly what she'll have.

10-Year Timeframe:

If Sarah doesn't need money for 10 years (retirement savings, long-term wealth building), share ETF likely better despite volatility.

10-Year Projection:

Term Deposit at 5.5% (assumes reinvesting):

• After 10 years: $50,000 × 1.055^10 = $86,219
• Before-tax gain: $36,219
• After 30% tax on gains: ~$60,953 final value

Share ETF at 8% average:

• After 10 years: $50,000 × 1.08^10 = $107,946
• Gain: $57,946
• After fees (0.5%) and PIE tax: ~$92,000 final value

Difference: ~$31,000 more from shares over 10 years (despite higher fees and tax)

Sarah's Decision:

Sarah splits her $50,000:

• $10,000 in savings account (emergency fund)
• $15,000 in 1-year term deposit (medium-term buffer)
• $25,000 in balanced fund (40% shares, 60% bonds) for long-term growth

This balances safety (emergency access, guaranteed returns) with growth potential (shares for long term).

Common Misunderstandings

Misunderstanding 1: "Past Returns Guarantee Future Returns"

Reality: Historical performance doesn't predict future results. Fund that returned 15% last year might return 5% or -10% next year. Use past returns as guide to typical range, not guarantee.

Misunderstanding 2: "Higher Return Always Better"

Reality: Higher returns usually come with higher risk. 12% return investment likely has years with -20% returns. Must match risk to timeframe and tolerance.

Misunderstanding 3: "Negative Year Means Bad Investment"

Reality: Share investments have negative years regularly but positive long-term average. Single bad year doesn't invalidate good long-term strategy. This is why matching timeframe to investment type matters.

Misunderstanding 4: "Fees Don't Matter Much"

Reality: Fees compound just like returns but work against you. 1% fee seems small but over 30 years reduces final value by ~25%. Always compare fees when choosing between similar investments.

Misunderstanding 5: "Inflation Doesn't Affect Me"

Reality: Inflation erodes purchasing power silently. "Safe" low-return investments can lose real value over time. Need to consider inflation when assessing if investment achieving goals.

Misunderstanding 6: "Volatility Equals Loss"

Reality: Volatility is fluctuation, not permanent loss. Share portfolio might drop 15% one year and rise 20% next. Only "lose" money if you sell during a down period. Long-term investors ride out volatility.

Misunderstanding 7: "Timing the Market Is Easy"

Reality: Consistently buying low and selling high is extremely difficult even for professionals. "Time in market beats timing the market" - staying invested long-term typically beats trying to jump in and out.

Final insight: Rate of return measures investment growth as percentage: [(Ending - Starting) ÷ Starting] × 100. Simple returns: profit not reinvested, linear growth. Compound returns: profit reinvested, exponential growth over time - dramatically more powerful (e.g., $10k at 5% for 30 years: simple = $25k, compound = $43k). Annualised return (CAGR) converts any timeframe to yearly rate for fair comparison between investments. Comparing investments requires assessing return, risk, timeframe, fees, tax treatment - not just return alone. Risk-return trade-off: higher potential returns come with higher volatility. Real return = nominal return minus inflation. Inflation erodes purchasing power - 5% return with 3% inflation = only 2% real growth. NZ scenario: $50k term deposit at 5.5% provides certainty, diversified ETF averaging 8% provides higher long-term growth with volatility. Common misunderstandings: past ≠ future, higher return ≠ always better, negative year ≠ bad investment, fees matter enormously, inflation affects everyone, volatility ≠ permanent loss, timing market extremely difficult. Understanding returns enables matching investments to goals, timeframe, and risk tolerance - foundation of sound investing.