How the numbers work: saving and investing

What is Risk in Financial Terms?

1. Low Risk Example:
2. Bank term deposit: $10,000 at 5.0% for 1 year
3. Outcome: Guaranteed $10,500 (excluding bank failure)
4. Range of outcomes: Very narrow (essentially certain)
5. Risk level: Very low
6. High Risk Example:
7. $10,000 invested in NZ shares portfolio
8. Possible 1-year outcomes: Anywhere from $7,000 to $15,000
9. Range of outcomes: Very wide (highly uncertain)
10. Risk level: High

What is Return in Financial Terms?

1. Return = (Ending Value - Starting Value + Income) ÷ Starting Value × 100

What is Return in Financial Terms?

1. Buy shares: $10,000
2. One year later value: $11,200
3. Dividends received: $300
4. Total return: ($11,200 - $10,000 + $300) ÷ $10,000 × 100 = 15%

Why Risk vs Return Matters in NZ Context

1. Starting balance: $10,000
2. Contributing: $3,000/year
3. Time horizon: 40 years until 65
4. Conservative fund (5% average return):
5. Age 65 balance: $382,000
6. Growth fund (9% average return):
7. Age 65 balance: $1,118,000
8. Difference: $736,000!
9. Cost of avoiding risk: Three-quarters of a million dollars

Common Misconceptions

1. Growth fund over 20 years:
2. • 95% of 20-year periods: Positive returns
3. • Average: +9% annually
4. • Worst 20-year period: Still +6% annually
5. • Risk = path volatility, not final destination

Common Misconceptions

1. $100,000 in savings account (3%) for 30 years:
2. Grows to: $242,726 nominal
3. But with 3% inflation, real value: $100,627
4. Gained almost nothing in purchasing power!
5. Same $100K in balanced fund (7%) for 30 years:
6. Grows to: $761,226 nominal
7. Real value: $315,827 (tripled purchasing power!)

Common Misconceptions

1. Portfolio of 50 NZ companies vs single company:
2. Specific risk: Reduced 90% (company failures average out)
3. Market risk: Unchanged (all fall in recession)
4. 2020 crash: Diversified NZ portfolio still dropped -25%

Why Time Changes Everything

1. $10,000 in growth fund
2. Best year: +25% = $12,500
3. Worst year: -20% = $8,000
4. Range: $4,500 (45% swing!)
5. Probability of loss: ~30%

Why Time Changes Everything

1. $10,000 in growth fund
2. Average outcome: $15,386 (+54%)
3. Bad scenario: $12,500 (+25%)
4. Excellent scenario: $19,000 (+90%)
5. Probability of loss: ~10%

Why Time Changes Everything

1. $10,000 in growth fund
2. Average outcome: $56,044 (+460%)
3. Conservative estimate: $38,000 (+280%)
4. Optimistic estimate: $85,000 (+750%)
5. Probability of loss: <1% (historically)

Volatility vs Actual Loss

1. January 2020: NZ50 index at 11,800
2. March 2020: Dropped to 8,800 (-25%)
3. $100,000 portfolio value: $75,000
4. Investor A (panicked):
5. Sold at $75,000 = Actual loss -$25,000
6. Permanently locked in loss
7. Investor B (stayed calm):
8. Held through volatility
9. December 2020: Index at 12,500 (+6% vs January)
10. Portfolio value: $106,000
11. Experienced volatility, but no actual loss
12. Ended +6% for year

Diversification: How It Works

1. Good year: +40%
2. Bad year: -50%
3. Bankruptcy risk: Lose 100%
4. Extreme volatility: ±50%

Diversification: How It Works

1. Good year: +20%
2. Bad year: -15%
3. Some companies fail, others thrive = averages out
4. Reduced volatility: ±20%

Diversification: How It Works

1. Good year: +18%
2. Bad year: -12%
3. Regional crashes offset by other regions
4. Further reduced volatility: ±15%

Asset Allocation: The Risk Dial

1. 80% Fixed income (bonds, term deposits)
2. 20% Growth (shares, property)
3. Expected return: 4-5%/year
4. Volatility: Low (±5%)
5. Worst year: -3%
6. Best for: Near-term goals, retirees, low risk tolerance

Asset Allocation: The Risk Dial

1. 50% Fixed income
2. 50% Growth
3. Expected return: 6-7%/year
4. Volatility: Moderate (±12%)
5. Worst year: -10%
6. Best for: Medium-term goals, balanced approach

Asset Allocation: The Risk Dial

1. 20% Fixed income
2. 80% Growth
3. Expected return: 8-9%/year
4. Volatility: High (±18%)
5. Worst year: -20%
6. Best for: Long-term goals, young investors, high tolerance

Asset Allocation: The Risk Dial

1. 5% Fixed income
2. 95% Growth
3. Expected return: 9-10%/year
4. Volatility: Very high (±22%)
5. Worst year: -30%
6. Best for: 20+ year horizons, strong stomach

🌍 Real-World NZ Risk vs Return Scenarios

1. Conservative choice costs: $704,000!
2. Over 40 years, growth fund gives 3x more money
3. Yes, growth fund will have scary drops:
4. • Probably 5-8 years with -10% to -25% returns
5. • Maybe 2-3 crashes of -30%+
6. • But 40 years is long enough to recover every time

Who this happens to, and what it meant for them

1. Extra $1,500/month to principal
2. Pays off mortgage in 18 years (vs 25 years)
3. Saves $125,000 in interest
4. Age 56: Mortgage-free
5. KiwiSaver age 65: $348,000 (conservative, 27 years)
6. Total wealth age 65: House ($1.2M) + KiwiSaver ($348K) = $1.55M

Who this happens to, and what it meant for them

1. $750/month extra to mortgage
2. $750/month to investments (balanced fund 7%)
3. Switch KiwiSaver to Balanced
4. Mortgage paid off in 21 years (vs 25)
5. Investment account age 65: $435,000
6. KiwiSaver age 65: $488,000 (balanced, higher returns)
7. Total wealth age 65: House ($1.2M) + Investments ($435K) + KiwiSaver ($488K) = $2.12M

1. Minimum mortgage payments
2. All $1,500/month to growth investments (9%)
3. Switch KiwiSaver to Growth
4. Mortgage paid off normal 25 years
5. Investment account age 65: $655,000
6. KiwiSaver age 65: $598,000 (growth)
7. Total wealth age 65: House ($1.2M) + Investments ($655K) + KiwiSaver ($598K) = $2.45M

1. Stay 100% Growth (risky near retirement):
2. Best case: $1,020,000 age 65
3. Average case: $850,000
4. Crash scenario: $520,000 (if crash year 6)
5. Glide path (reducing risk):
6. Best case: $870,000 age 65
7. Average case: $740,000
8. Crash scenario: $660,000 (protected by conservative allocation)

Who this happens to, and what it meant for them

1. Return: 5%/year
2. 10 years: $77,641
3. 20 years: $205,753
4. Volatility: None
5. Risk: Inflation (real return only 2%)

Who this happens to, and what it meant for them

1. Return: 9%/year average
2. 10 years: $96,476
3. 20 years: $334,924
4. Volatility: High (±20% years)
5. Risk: Market drops (but time to recover)

1. Return: 7%/year average
2. 10 years: $86,732
3. 20 years: $260,913
4. Volatility: Moderate (±12%)
5. Risk: Balanced between options 1 and 2

Step 1: Calculate Your Target

1. Essential monthly expenses: $4,300
2. Target: 6 months coverage
3. Emergency fund goal = $4,300 × 6

= $25,800

Step 3: Automate Your Savings

1. Net monthly income: $5,500
2. Save 10% automatically: $550/month
3. Time to reach $25,800: 47 months (4 years)
4. Increase to 15%: $825/month
5. Time to reach $25,800: 31 months (2.6 years)

Step 3: Automate Your Savings

1. Save $500/month
2. Time to reach $25,800: 52 months (4.3 years)
3. Save $750/month
4. Time to reach $25,800: 34 months (2.8 years)

Building During Different Life Stages

1. Income: $3,500/month net
2. Essential expenses: $2,200/month
3. Target (3 months): $6,600
4. Save 15% ($525/month)
5. Time to goal: 13 months

Building During Different Life Stages

1. Combined income: $7,500/month net
2. Essential expenses: $5,200/month
3. Target (6 months): $31,200
4. Save 12% ($900/month)
5. Time to goal: 35 months

Building During Different Life Stages

1. Income: $6,000/month net
2. Essential expenses: $3,800/month (lower, mortgage paid)
3. Target (9 months): $34,200 (higher for age)
4. Save 18% ($1,080/month)
5. Time to goal: 32 months

🌍 Real-World Emergency Fund Stories

1. Emergency fund balance: $18,000
2. Monthly essential expenses: $3,200
3. Coverage: 5.6 months
4. Severance pay: 2 months salary ($10,000)
5. Total runway: 8.7 months

Who this happens to, and what it meant for them

🌍 Real-World Emergency Fund Stories

1. Emergency fund used: $8,000
2. Remaining balance: $10,000
3. Time unemployed: 4 months
4. Debt incurred: $0

🌍 Real-World Emergency Fund Stories

1. Emergency fund balance: $22,000
2. Monthly expenses: $4,100
3. Coverage: 5.4 months

Who this happens to, and what it meant for them

1. Used emergency fund: $9,500
2. Remaining balance: $12,500
3. Still had 3 months coverage
4. Interest paid on debt: $0

1. Normal monthly income: $8,000
2. Lost client revenue: $4,000/month (50% of income)
3. New income: $4,000/month
4. Essential expenses: $4,500/month
5. Monthly shortfall: $500
6. Emergency fund: $45,000 (10 months at full expenses)

Who this happens to, and what it meant for them

1. Months 1-3: $500 × 3 = $1,500
2. Month 4: slight surplus, no draw
3. Total emergency fund used: $1,500
4. Remaining balance: $43,500

1. Emergency fund: $0
2. Monthly income: $3,800
3. Monthly expenses: $3,750
4. Monthly surplus: $50 (barely surviving)
5. Credit card debt: $2,500

Who this happens to, and what it meant for them

1. Emergency fund: $7,100
2. Essential monthly expenses: $2,400 (reduced from $3,750)
3. Coverage: 3 months (goal achieved!)
4. Credit card debt: $1,200 (paid down $1,300)

&#128290; Worked Examples

1. Interest avoided in the first year: $5,000 x 22.95% = $1,147.50
2. This saving is guaranteed and is not taxed

Card cleared, $1,147.50 kept for certain

Who this happens to, and what it meant for them

&#128290; Worked Examples

1. Expected fund gain: $5,000 x 7% = $350 (not guaranteed)
2. Less PIE tax at 28%: $350 x 0.72 = $252 after tax
3. Card interest still charged: $5,000 x 22.95% = $1,147.50

Net position: $252 - $1,147.50 = about $895.50 worse off

&#128290; Worked Examples

1. Government contribution earned: $500 x 25% = $125
2. Maximum available: $260.72 (needs $1,042.86 contributed)

Still on the table: $260.72 - $125 = $135.72

Who this happens to, and what it meant for them

&#128290; Worked Examples

1. Top-up needed: $1,042.86 - $500 = $542.86
2. Extra government money: $542.86 x 25% = $135.72

That is an instant 25% return before any market movement

1. Guaranteed, tax-free saving: $10,000 x 5.99% = $599 in the first year
2. The saving is certain and shortens the loan

Who this happens to, and what it meant for them

1. To beat the mortgage after 28% PIE tax, a fund must earn:
2. 5.99% / 0.72 = about 8.3% before tax, every year
3. A 7% fund after 28% tax is 7% x 0.72 = 5.04%, below 5.99%

On return alone, paying the 5.99% mortgage wins, with no risk

1. Three months of essentials: $2,600 x 3 = $7,800
2. Current savings: $6,000

Gap to fill first: $7,800 - $6,000 = $1,800

Who this happens to, and what it meant for them

1. If he invests all $6,000 and then loses hours or faces a big bill:
2. He may have to sell shares in a downturn, locking in a loss
3. Or reach for a credit card at 20% or more, undoing his progress

Top the fund to $7,800 first, then invest the surplus

What round-ups are worth in a year

1. Per month: 40 transactions x $0.50 = $20.00
2. Per year: $20.00 x 12 = $240.00

$240.00 a year, which is real money and is also the whole of it.

The fee that eats it

1. Fee: $3.00 a month x 12 = $36.00 a year
2. Saved by round-ups: $240.00 a year
3. Fee as a share of what you saved: $36.00 / $240.00 = 15.0%

15 percent of everything you put in, before any investment return exists to pay it from.

Where a real gain comes from

1. At 0.10%: $10,000.00 x 0.10% = $10.00 a year
2. At 4.00%: $10,000.00 x 4.00% = $400.00 a year
3. Gain from moving it: $400.00 - $10.00 = $390.00 a year
4. After resident withholding tax at 33%: $390.00 x 0.67 = $261.30

$261.30 a year, after tax, for one afternoon of paperwork, done once.

The one nudge that beats round-ups on its own terms

1. Round-ups: $20.00 a month, arriving in scattered cents
2. Payday transfer of $50.00: $50.00 a month, arriving before you see it
3. Difference over a year: ($50.00 - $20.00) x 12 = $360.00

Same psychology, two and a half times the amount, no fee.

The KiwiSaver comparison, for scale

1. One percentage point: $70,000.00 x 1% = $700.00 a year
2. Against round-ups: $700.00 / $240.00 = 2.9 times as much

Nearly three times the round-up total, from one change, once.

Questions to ask before signing up

1. What is the fee, in dollars per year? Not as a percentage, which flatters flat fees.
2. What will I actually save per year? Multiply your real transaction count by 50 cents.
3. What is the fee as a share of that? Above 5 percent deserves a hard look.
4. What rate does the balance earn , and how does it compare with a plain savings account?
5. Could I get the same effect free with an automatic transfer at my existing bank?

The last question ends most of these decisions.

🔢 Four worked examples

1. Future value factor: ((1.05 to the power of 18) − 1) ÷ 0.05 = 28.132
2. Balance at 18: $1,040 × 28.132 = $29,257
3. Total contributed: $1,040 × 18 = $18,720

Balance about $29,250, of which about $10,530 is growth on top of what the family put in.

Who this happens to, and what it meant for them

🔢 Four worked examples

1. Her own contribution: $12,000 × 3.5% = $420
2. Employer contribution (3.5% from 1 April 2026): $12,000 × 3.5% = $420, before employer superannuation contribution tax (ESCT) is deducted
3. Government contribution: 25 cents per $1, so $420 × 25% = $105 (her $420 is below the $1,042.86 needed for the full $260.72)

About $945 added in the year, of which roughly $525 is employer and government money on top of her own $420.

Who this happens to, and what it meant for them

1. $500 × 10.5% = $52.50

The child keeps $500 − $52.50 = $447.50

Who this happens to, and what it meant for them

1. At a parent's 33% marginal rate: $500 × 33% = $165

Using the child's own 10.5% PIR saves $165 − $52.50 = $112.50 in that single year.

1. Default PIR of 28%: $500 × 28% = $140
2. Correct child PIR of 10.5%: $500 × 10.5% = $52.50

The missing IRD number costs $140 − $52.50 = $87.50 that year.

Who this happens to, and what it meant for them

The daily calculation, step by step

1. Step 1. Take the annual rate and divide by 365 to get a daily rate. At 4.5 percent that is 0.0123 percent a day.
2. Step 2. Apply it to the closing balance each day. On $10,000 that is $1.2329 a day .
3. Step 3. Add up the days in the month. A 31 day month gives $38.22 ; a 28 day February gives $34.52 .
4. Step 4. Deduct RWT at your rate. At 17.5 percent that is $6.69.

$31.53 is credited to your account. The bank pays the $6.69 to Inland Revenue on your behalf.

What to do this week

1. 1. Log in to each bank and find the tax settings on every interest bearing account.
2. 2. Check an IRD number is recorded. If not, that account is on 45 percent.
3. 3. Check the RWT rate matches your income tax rate. If nothing was ever chosen, it is on 33 percent.

On a $10,000 balance at 4.5 percent, those two checks are worth up to $123.75 a year.

What the gap is actually worth

1. Term deposit, 39 percent RWT: $2,500 less $975 of tax leaves $1,525 .
2. Term PIE, 28 percent PIR: $2,500 less $700 of tax leaves $1,800 .

The PIE keeps $275 more from exactly the same $2,500, which is 18 percent more in the hand.

What to do with this

1. 1. Check what RWT rate each of your interest bearing accounts is actually using, at every bank.
2. 2. If any is on 33 percent by default or 45 percent for want of an IRD number, fix it.
3. 3. Find your PIR using Inland Revenue's tool rather than estimating it, and tell your provider if it has changed.
4. 4. Compare offers after tax at your own rates, not on the advertised headline.

If your rate is 30, 33 or 39 percent, a term PIE is worth pricing properly. If it is 10.5 or 17.5, decide on rate and terms instead.

Dividend Yield Explained

1. Dividend Yield = (Annual Dividend per Share ÷ Current Share Price) × 100

How It Works

1. You invest, say, $200 every payday
2. When prices are high, $200 buys fewer units
3. When prices are low, $200 buys more units
4. Your average purchase price evens out over time

The discount to net asset value

1. Net tangible assets per share: $1.50
2. Market price: $1.20
3. Discount: ($1.50 - $1.20) / $1.50 = 20%

You are buying property at 80 cents in the dollar of its valuation.

Gross Dividend and Your Rate

1. Cash dividend, say $72
2. Plus imputation credits of, say, $28
3. Gross dividend $100, taxed at 33% is $33
4. Credits cover $28, so about $5 of RWT is withheld