Core answer: To reach a goal G in n months with return r/yr: monthly saving = G × i ÷ ((1+i)ⁿ − 1), where i = r/12. Goal ¥100,000 in 2 years at 3%: monthly = 100,000 × 0.0025 ÷ (1.0025²⁴ − 1) = 250 ÷ 0.0618 ≈ ¥4,045/month. Without any return: ¥4,167/month — returns shorten the path, but for short goals the heavy lifting is always the savings rate.
The two directions
- Goal → monthly saving: PMT = G × i ÷ ((1+i)ⁿ − 1)
- Monthly saving → future value: FV = PMT × ((1+i)ⁿ − 1) ÷ i
| Goal ¥100k | 1 yr | 2 yr | 3 yr | 5 yr |
|---|---|---|---|---|
| @0% | ¥8,333 | ¥4,167 | ¥2,778 | ¥1,667 |
| @3% | ¥8,212 | ¥4,045 | ¥2,687 | ¥1,562 |
| @6% | ¥8,107 | ¥3,932 | ¥2,588 | ¥1,466 |
Worked examples
Example 1 — House down payment. Target ¥600k in 4 years at 3%: monthly = 600,000 × 0.0025 ÷ (1.0025⁴⁸ − 1) = 1,500 ÷ 0.1273 ≈ ¥11,788/month. If that's above capacity, the honest options are: more time (5 yr → ¥9,369), lower target, or higher income — not higher risk on money needed in 4 years.
Example 2 — Emergency fund first. 3–6 months of expenses (¥5,000/mo expenses → ¥15–30k) BEFORE any investing goal; at ¥2,000/month you're done in 8–15 months.
Example 3 — The automation trick. Transfer on payday, not month-end: "save what's left after spending" reliably equals zero; "spend what's left after saving" works. Pay-yourself-first is the whole behavioral game.
Example 4 — Windfall allocation. ¥50k year-end bonus toward the ¥600k goal: new monthly need drops to ¥10,790 — one bonus ≈ 1 month of savings effort per year.
Common mistakes and myths
- Investing short-term goals in volatile assets — money needed within 3 years belongs in deposits/money funds; a −20% year right before the down payment is unrecoverable.
- Ignoring inflation on long goals — ¥300k for a child's college in 15 years needs ~¥400k at 2% inflation; inflate the TARGET, not just the return.
- Setting monthly saves you can't sustain — a plan at 60% of take-home dies in month 3; start at 15–25%, ratchet up with raises.
- Counting expected raises — plans built on hoped income collapse on job changes; baseline the plan on current income, treat raises as accelerants.
- Mixing goals in one account — separate sub-accounts (or sub-funds) per goal prevent the "borrow from the house fund" leak.