💡
Learning My Way
Tutoring with a Twist
📅 Exam
4 to 5 Nov 2026
Home › Investing & Planning › Financial Planning
Unit 4 · Investing & Planning

🎯 Financial Planning

The capstone topic, combining everything. Regular savings contributions, compound growth, loans, and goals. The core tool is the future value of a regular savings plan (annuity), used to work backwards from a target to a required weekly or annual deposit.

Capstone of all finance topics
FV annuity formula: PMT × [(1+r)ⁿ−1]/r
Verify: break into individual payments
This is the final topic, everything connects here. You'll use compound interest from Unit 3, annuities, and loan knowledge together. Make sure annuities and compound investments are solid before you tackle this page.
1

The tools in a financial plan

💰

Compound Interest

Lump sum grows over time. FV = PV(1+r)ⁿ

📅

Regular Savings

Equal contributions at regular intervals, annuity formula

🏦

Loans

Reducing balance, repayments over time, total interest

Financial planning questions combine these tools. A typical exam question might ask: "Sarah wants to save $30,000 for a house deposit in 5 years. She invests a lump sum and makes regular contributions. What total does she accumulate?"

The key is identifying which tool applies to which part, lump sum → compound interest, regular deposits → annuity formula.

2

Future value of regular contributions

When you deposit the same amount at the end of each period, the total you accumulate is the sum of each deposit grown with compound interest. The formula adds all those future values at once.

Future Value of Regular Contributions (Ordinary Annuity) FV = PMT × [ (1 + r)ⁿ − 1 ] / r
PMT = regular payment · r = interest rate per period · n = number of periods

How to verify with clean numbers: multiply the result you expect by r, add 1, subtract (1+r)ⁿ, and check it equals zero, or just verify by adding up the individual contributions grown with compound interest.

Worked Example A · basic annuity FV

$100 is deposited at the end of each year for 2 years into an account earning 10% p.a. Find the total accumulated.

Formula:FV = 100 × [(1.10)² − 1] / 0.10
Calculate:= 100 × [1.21 − 1] / 0.10 = 100 × 0.21 / 0.10 = 100 × 2.1 = $210

Verify by tracking each deposit:

DepositWhen depositedGrows forValue at end
$100End of year 11 year$100 × 1.10 = $110
$100End of year 20 years$100 × 1.00 = $100
Total$210 ✓
Worked Example B · 3-year savings plan

$200 deposited annually for 3 years at 10% p.a. Find the accumulated amount.

Formula:FV = 200 × [(1.10)³ − 1] / 0.10
Calculate:= 200 × [1.331 − 1] / 0.10 = 200 × 0.331 / 0.10 = 200 × 3.31 = $662

Verify:

Year 1 deposit:$200 × (1.10)² = $200 × 1.21 = $242
Year 2 deposit:$200 × (1.10)¹ = $200 × 1.10 = $220
Year 3 deposit:$200 × (1.10)⁰ = $200 × 1.00 = $200
Total:$242 + $220 + $200 = $662 ✓
3

Planning to reach a savings goal

If you know the target FV and want to find the required annual deposit PMT, rearrange the formula:

Finding required PMT PMT = FV × r / [ (1 + r)ⁿ − 1 ]
Worked Example C · finding the required deposit

You want to save $2,200 over 2 years by depositing equal amounts annually at 20% p.a. How much must you deposit each year?

Rearranged:PMT = 2,200 × 0.20 / [(1.20)² − 1]
Calculate:= 2,200 × 0.20 / [1.44 − 1] = 440 / 0.44 = $1,000/year
Check:1,000 × [(1.2)² − 1] / 0.2 = 1,000 × 2.2 = $2,200 ✓
4

Superannuation, the big financial plan

Superannuation is a long-term retirement savings plan. Employers contribute a percentage of your salary (currently 11%), and you can add voluntary contributions. It works like a regular savings annuity over 40+ years, with compound growth.


Key features:
  • Regular contributions (employer + voluntary)
  • Compound growth over decades
  • Small early contributions = big results
Exam tip:

Super questions use the FV annuity formula. Identify the annual contribution (PMT), annual rate (r), and years to retirement (n). Then apply FV = PMT × [(1+r)ⁿ − 1] / r.

The power of starting early: $1,000/year at 10% for 30 years → FV = $164,494. Starting 10 years later (20 years) → FV = $57,275. Those 10 extra years almost triple the outcome. This is why early investing is a common exam context.

Practice Questions

1. Find the future value when $100 is deposited annually at 10% p.a. for 2 years. ▶
FV = 100 × [(1.10)² − 1] / 0.10 = 100 × 0.21 / 0.10 = 100 × 2.1 = $210
2. $200 is deposited at the end of each year for 3 years at 10% p.a. Find the accumulated value. ▶
FV = 200 × [(1.10)³ − 1] / 0.10 = 200 × 0.331 / 0.10 = 200 × 3.31 = $662
3. $1,000 is deposited annually for 2 years at 20% p.a. Use the annuity formula to find the FV, then verify by tracking each deposit. ▶
Formula: FV = 1,000 × [(1.20)² − 1] / 0.20 = 1,000 × 0.44 / 0.20 = 1,000 × 2.2 = $2,200

Verify:
Deposit 1: $1,000 × 1.20¹ = $1,200
Deposit 2: $1,000 × 1.20⁰ = $1,000
Total = $1,200 + $1,000 = $2,200 ✓
4. $500 is deposited annually for 2 years at 10% p.a. Find the FV. ▶
FV = 500 × [(1.10)² − 1] / 0.10 = 500 × 0.21 / 0.10 = 500 × 2.1 = $1,050
5. A person invests $1,000 at 30% p.a. compounded annually. After how many years is the investment worth $2,197? (Check by trial.) ▶
FV = PV × (1+r)ⁿ = 1,000 × (1.30)ⁿ
Try n = 1: 1,000 × 1.30 = 1,300 ✗
Try n = 2: 1,000 × 1.69 = 1,690 ✗
Try n = 3: 1,000 × 2.197 = 2,197 ✓ → 3 years

🌏 Ready to test yourself?

Life Plan escape room, 6 financial planning challenges to unlock your future.

Open Escape Room →