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🌏 Life Plan Escape
Unit 4 · Financial Planning
📋

The Planner is Down

Six clients are waiting for their financial projections. The planning software has crashed and their retirement, savings, and investment goals are all stuck mid-calculation. Work through each projection manually, their futures depend on it.

Projections done
0% 0 / 6 complete
1
Client 1, 2-year savings plan
Client deposits $100 at the end of each year for 2 years into an account earning 10% p.a.

Use the annuity formula to find the total accumulated value.
(FV = PMT × [(1+r)ⁿ − 1] / r)
FV = 100 × [(1.10)² − 1] / 0.10 = 100 × 0.21 / 0.10 = 100 × 2.1
✓ Correct, FV = $210
2
Client 2, 3-year savings plan
Client deposits $200 at the end of each year for 3 years at 10% p.a.

Find the accumulated value at the end of 3 years.
FV = 200 × [(1.10)³ − 1] / 0.10. Note: (1.10)³ = 1.331
✓ Correct, FV = $662
3
Client 3, high-growth 2-year plan
Client invests $1,000 per year for 2 years in a high-growth fund returning 20% p.a.

What is the future value?
FV = 1,000 × [(1.20)² − 1] / 0.20. (1.20)² = 1.44, so [(1.44−1)/0.20] = ?
✓ Correct, FV = $2,200
4
Client 4, medium savings, 2 years
Client contributes $500 annually for 2 years at 10% p.a.

Find the total accumulated.
FV = 500 × [(1.10)² − 1] / 0.10 = 500 × 2.1
✓ Correct, FV = $1,050
5
Client 5, investment growth projection
Client invests a lump sum of $1,000 at 30% p.a. compounded annually. The projection shows it grows to $2,197.

How many years does this take? (Try small whole numbers)
FV = 1,000 × (1.30)ⁿ. Try: 1.30¹=1.3 · 1.30²=1.69 · 1.30³=?
✓ Correct, 3 years (1.30³ = 2.197)
6
Client 6, retirement savings, 3 years
The final client is starting a 3-year super top-up plan: $100 per year at 10% p.a.

What does the account hold at the end of 3 years?
FV = 100 × [(1.10)³ − 1] / 0.10 = 100 × 0.331 / 0.10 = 100 × 3.31
✓ Correct, FV = $331

🌏 ALL PLANS DELIVERED

Six clients. Six futures. Every projection calculated, every plan filed. The system comes back online with the numbers intact. Financial planning, sorted.

FV = PMT × [(1+r)ⁿ−1] / r
PMT = FV × r / [(1+r)ⁿ−1]
verify by tracking deposits
lump sum → FV = PV(1+r)ⁿ
start early = more growth
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