Savings Strategies

TipHow these exercises work

Each topic starts with a real scenario and a bar model, then three levels of exercises. Level 1 (Guided) fills in the blanks of a finished function. Level 2 (Practice) applies it to new numbers. Level 3 (Challenge) asks a new question with little scaffolding. The R and Python exercises run in your browser: click Run Code to try, Submit Answer to check, and use the hint or solution if you get stuck. Excel exercises have a solution you can reveal.

1 Book Topics

  • Savings rate: the one number to track; it sets the speed of wealth building more than income does (a $40,000 earner saving 40% reaches $500k in 18 years, a $120,000 earner saving 10% takes 21)
  • Benchmarks: under 10% danger zone; 10 to 20% average; 20 to 30% strong; 30%+ path to financial independence within a decade or two
  • Make savings automatic: automate transfers the day after payday, use a separate bank, label each account by purpose, and track progress visually
  • Savings and the FOO: saving shows up at nearly every step of the Financial Order of Operations; the right rate is the one you can keep up for decades
  • Account types: high yield savings and money market accounts for emergency and sinking funds, CDs for known future goals, regular savings to avoid
  • FDIC insurance: covers up to $250,000 per account holder per bank; spread larger balances across banks

2 Savings Rate

The savings rate is the slice of your income bar that goes to savings. Every dollar goes to either spending or savings, so the rate measures how big the savings slice is.

Formula: Savings Rate = (Income − Spending) ÷ Income × 100

Example: you take home $5,000 and spend $3,500. (5,000 − 3,500) ÷ 5,000 = 30% savings rate.

Savings slice as a percentage of income (same $60k income, different rates)

Savings slice as a percentage of income (same $60k income, different rates)

Savings slice as a percentage of income (same $60k income, different rates)

Savings slice as a percentage of income (same $60k income, different rates)

How to read this result: a 30% rate means 30 cents of every dollar you bring home stays with you. If the rate is negative, you are spending more than you earn and the gap is coming from savings or debt.

2.1 Level 1: Guided

Fill in the blanks to finish savings_rate(), then find the savings rate when you take home $5,000 and spend $3,500.

Put income in A2 (5000) and spending in B2 (3500). Find the savings rate in C2.

=(A2 - B2) / A2 * 100

This returns 30.

What you save is what you earn minus what you spend.

def savings_rate(income, spending):
    return ((income - spending) / income) * 100

savings_rate(5000, 3500)

What you save is what you earn minus what you spend.

savings_rate <- function(income, spending) {
  ((income - spending) / income) * 100
}
savings_rate(5000, 3500)

2.2 Level 2: Practice

Flip the formula. To save 25% of a $5,000 paycheck, what is the most you can spend? Spending = Income × (1 − Rate).

Put income in A2 (5000) and the target rate in B2 (0.25). Find the spending limit in C2.

=A2 * (1 - B2)

This returns $3,750.

Write 25% as 0.25. The share you can spend is 1 - target_rate.

def spending_limit(income, target_rate):
    return income * (1 - target_rate)

spending_limit(5000, 0.25)

Write 25% as 0.25. The share you can spend is 1 - target_rate.

spending_limit <- function(income, target_rate) {
  income * (1 - target_rate)
}
spending_limit(5000, 0.25)

2.3 Level 3: Challenge

Label each spending level on a $5,000 income with the book’s tier: under 10% is “Danger zone”, 10% to under 20% “Average”, 20% to under 30% “Strong”, and 30% or more “FI path”. Spending levels: $4,700, $4,250, $3,750, $3,250, and $5,200.

Put spending in A2:A6, the rate in B2:B6, and the tier in C2:C6.

In B2, filled down: =(5000-A2)/5000*100. In C2, filled down:

=IFS(B2 < 10, "Danger zone", B2 < 20, "Average", B2 < 30, "Strong", TRUE, "FI path")

The tiers are Danger zone, Average, Strong, FI path, Danger zone. The last one spends more than it earns (-4%).

np.select() checks conditions in order: [rate < 10, rate < 20, rate < 30] with labels ["Danger zone", "Average", "Strong"] and default="FI path". Finish with .tolist().

levels["rate"] = savings_rate(5000, levels["spending"])
rate = levels["rate"]
levels["tier"] = np.select(
    [rate < 10, rate < 20, rate < 30],
    ["Danger zone", "Average", "Strong"],
    default="FI path"
)
levels["tier"].tolist()

case_when() checks in order: rate < 10 ~ "Danger zone", then rate < 20, then rate < 30, then .default = "FI path". Finish with pull(tier).

levels |>
  mutate(
    rate = savings_rate(5000, spending),
    tier = case_when(
      rate < 10 ~ "Danger zone",
      rate < 20 ~ "Average",
      rate < 30 ~ "Strong",
      .default = "FI path"
    )
  ) |>
  pull(tier)

3 Years to a Savings Target

The book compares two savers at a 7% return. One earns $40,000 and saves 40% ($16,000 a year). The other earns $120,000 and saves 10% ($12,000 a year). The bigger saver reaches $500,000 first. We can solve for the number of years directly.

Formula: Years = ln(1 + Target × r ÷ Annual Savings) ÷ ln(1 + r)

Example: ln(1 + 500,000 × 0.07 ÷ 16,000) ÷ ln(1.07) = 17.1 years, so the balance passes $500k during year 18. At $12,000 a year it takes 20.2 years, so year 21.

Years to reach $500,000 at a 7% return on a $60,000 income

Years to reach $500,000 at a 7% return on a $60,000 income

Years to reach $500,000 at a 7% return on a $60,000 income

Years to reach $500,000 at a 7% return on a $60,000 income

How to read this result: the answer is the number of years of steady saving needed, not counting anything you already have. Raising the savings rate shortens the timeline much more at low rates than at high ones.

3.1 Level 1: Guided

Fill in the blanks to finish years_to_target(), then find how long $16,000 a year at 7% takes to reach $500,000.

Put yearly savings in A2 (16000), the target in B2 (500000), and the return in C2 (0.07). Find the years in D2.

=NPER(C2, -A2, 0, B2)

This returns about 17.1 years.

The formula is ln(1 + Target × r ÷ Annual Savings) ÷ ln(1 + r).

import math
def years_to_target(annual_savings, target, rate=0.07):
    return math.log(1 + target * rate / annual_savings) / math.log(1 + rate)

years_to_target(16000, 500000)

The formula is ln(1 + Target × r ÷ Annual Savings) ÷ ln(1 + r).

years_to_target <- function(annual_savings, target, rate = 0.07) {
  log(1 + target * rate / annual_savings) / log(1 + rate)
}
years_to_target(16000, 500000)

3.2 Level 2: Practice

A higher earner saves $12,000 a year (10% of $120,000). In which year does the balance pass $500,000?

Change A2 to 12000 and round up.

=ROUNDUP(NPER(C2, -A2, 0, B2), 0)

This returns 21, four years after the $40,000 earner saving 40%.

Round up with math.ceil(); the balance passes the target during that year.

math.ceil(years_to_target(12000, 500000))

Round up with ceiling(); the balance passes the target during that year.

ceiling(years_to_target(12000, 500000))

3.3 Level 3: Challenge

On a $60,000 income, what is the smallest whole-percent savings rate (from 5% to 50%) that reaches $500,000 within 20 years at 7%? Give it as a decimal.

Find the yearly savings needed, divide by income, and round up to the next whole percent.

=ROUNDUP(PMT(7%, 20, 0, -500000) / 60000, 2)

PMT() says you need $12,196 a year, which is 20.3% of income, so 21%.

Yearly savings is 60000 * r. Use min(r for r in rates if years_to_target(60000 * r, 500000) <= 20).

rates = [r / 100 for r in range(5, 51)]
min(r for r in rates if years_to_target(60000 * r, 500000) <= 20)

years_to_target() is vectorized: pass 60000 * rates, then use min(rates[...]).

rates <- seq(0.05, 0.50, by = 0.01)
years <- years_to_target(60000 * rates, 500000)
min(rates[years <= 20])