Savings Goals

# Savings Goals

## Core Concepts

### Required Monthly Savings
To accumulate a future value FV in n periods at rate r per period:

PMT = FV × r / [(1+r)^n - 1]

This is the sinking fund formula (future value of annuity solved for PMT).

### Inflation-Adjusted Targets
Always compute goals in future (nominal) dollars:

FV_nominal = FV_today × (1 + inflation)^years

Then solve for the required savings using the nominal return, or use the real return with today's dollars.

### Education Funding
- **529 plans**: tax-free growth for qualified education expenses, state tax deductions in many states
- **Current costs** (2025-26, total cost of attendance, College Board Trends in College Pricing): ~$30K/year (public four-year in-state) to ~$65K/year (private nonprofit), growing ~5%/year
- **Front-loading**: maximize early contributions for compound growth
- **Superfunding**: 5-year gift tax averaging (contribute 5× annual exclusion at once)
- **Financial aid impact**: parent-owned 529 assets are assessed at a maximum of 5.64% in the federal Student Aid Index (SAI) formula — FAFSA has used the SAI in place of the Expected Family Contribution (EFC) since the 2024-25 award year

### Retirement Accumulation
- **Target nest egg**: annual spending need / safe withdrawal rate
  - Example: $80K/year spending / 0.04 = $2,000,000
- **Safe withdrawal rate**: traditionally 4% (Bengen rule), adjusted for fees, taxes, longevity
- **Required savings rate**: depends on starting age, current savings, expected returns
- **Employer match**: always capture full match — it's an immediate 50-100% return
- **Catch-up contributions**: additional 401(k)/IRA contributions allowed after age 50

### Down Payment Saving
- Typical target: 20% of home price (avoids PMI)
- Timeline: typically 2-7 years → conservative allocation (HYSA, short-term bonds)
- Include closing costs (2-5% of purchase price) in savings target

### Goal Priority Framework
Recommended priority order:
1. Emergency fund (3-6 months expenses)
2. Employer 401(k) match (free money)
3. High-interest debt payoff (>6-8% rate)
4. HSA (triple tax advantage if eligible)
5. Max retirement accounts (401k, IRA, Roth)
6. Education funding (529)
7. Other goals (home, vacation, etc.)

### Multiple Goal Balancing
- Allocate savings across goals based on priority, timeline, and flexibility
- Non-negotiable goals (retirement) take precedence over flexible goals
- Shorter timelines need more conservative investment allocation
- Use goal-based investing: separate sub-portfolios per goal with appropriate risk

### Savings Rate Benchmarks
- Minimum: 15% of gross income for retirement (including employer match)
- Aggressive: 25-50%+ for early retirement / FIRE
- Savings rate = total savings / gross income

## Key Formulas

| Formula | Expression | Use Case |
|---------|-----------|----------|
| Required savings (PMT) | PMT = FV × r / [(1+r)^n - 1] | Monthly savings for a goal |
| Future value with savings | FV = PV(1+r)^n + PMT×[(1+r)^n - 1]/r | Project goal balance |
| Inflation adjustment | FV_real = FV_today × (1+π)^t | Convert today's dollars to future |
| Retirement target | Nest egg = annual spend / SWR | Size the retirement goal |
| Years to goal | n = ln(FV×r/PMT + 1) / ln(1+r) | How long until goal is funded |
| Savings rate | SR = total savings / gross income | Track savings discipline |

## Worked Examples

### Example 1: College Savings (529)
**Given:** Need $200,000 in 18 years, expect 7% annual return, starting from $0
**Calculate:** Required monthly savings
**Solution:**
- Monthly rate: r = 0.07/12 = 0.005833
- Months: n = 18 × 12 = 216
- PMT = $200,000 × 0.005833 / [(1.005833)^216 - 1]
- PMT = $1,166.67 / [3.5125 - 1]
- PMT = $1,166.67 / 2.5125 = **$464.34/month**

### Example 2: Retirement Accumulation
**Given:** Age 30, $50,000 currently saved, wants $2,000,000 by age 65, expects 8% annual return
**Calculate:** Required monthly savings
**Solution:**
- Monthly rate: r = 0.08/12 = 0.006667; months: n = 35 × 12 = 420
- FV of current savings (monthly compounding): $50,000 × (1.006667)^420 = $50,000 × 16.2925 = $814,627
- Remaining needed: $2,000,000 - $814,627 = $1,185,373
- PMT = $1,185,373 × 0.006667 / [(1.006667)^420 - 1]
- PMT = $7,902.49 / [16.2925 - 1]
- PMT = $7,902.49 / 15.2925 = **$517/month**
- With employer match of $200/mo: personal contribution = **$317/month**

## Common Pitfalls
- Not inflation-adjusting future goals (college in 18 years costs much more than today)
- Neglecting employer match — it's the highest guaranteed return available
- Too conservative allocation for long-horizon goals (20+ years can tolerate equity risk)
- Saving for college before adequately funding retirement (retirement has no financial aid)
- Not revisiting savings rate as income grows (lifestyle creep absorbs raises)
- Using average returns without considering sequence risk near goal date

## Cross-References
- **time-value-of-money** (core plugin, Layer 0): FV/PV calculations, annuity formulas
- **emergency-fund** (wealth-management plugin, Layer 6): must be funded before other goals
- **debt-management** (wealth-management plugin, Layer 6): high-interest debt payoff competes with savings
- **tax-efficiency** (wealth-management plugin, Layer 5): 529 tax benefits, Roth vs traditional, HSA
- **investment-policy** (wealth-management plugin, Layer 5): goal-based allocation aligns with IPS constraints
- **asset-allocation** (wealth-management plugin, Layer 4): glide paths for target-date retirement savings
- **finance-psychology** (wealth-management plugin, Layer 7): mental accounting, present bias, commitment devices
- **financial-planning-workflow** (advisory-practice plugin, Layer 10): savings goals are key inputs to the comprehensive financial planning process

## Running the script
Run the reference implementation directly:

```
uv run scripts/savings_goals.py      # PEP 723 header resolves dependencies automatically
python3 scripts/savings_goals.py     # standard library only — no installs needed
```

A bare run prints a demo covering required monthly savings, retirement accumulation, time-to-goal, inflation adjustment, shortfall analysis, education funding, savings rate, and real returns. Use `--verify` to recompute the demo figures and assert they match this skill's worked examples (prints PASS/FAIL, exits nonzero on mismatch), and `--help` to list the available classes and functions. The file is primarily meant to be imported as a module (`from savings_goals import SavingsGoals`) rather than run standalone.