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🔐 Market Vault Escape
Unit 4 · Compound Investments
💜

The Vault Sequence

A market analyst is locked in the secure vault after a system lockdown. The biometric override requires six investment calculations to be solved in sequence, each correct answer unlocks the next security layer. You're the only one on the outside who can help.

Layers unlocked
0% 0 / 6 solved
1
Layer 1, basic future value
The first security code is the future value of an investment.

$1,000 is invested at 10% p.a. compounded annually for 3 years.

What is the future value (to the nearest dollar)?
FV = PV × (1 + r)ⁿ = 1,000 × (1.10)³. Work out 1.10³ first.
✓ Correct, FV = $1,331
2
Layer 2, higher rate, fewer years
$2,000 invested at 20% p.a. compounded annually for 2 years.

Find the future value (to the nearest dollar).
FV = 2,000 × (1.20)². (1.20)² = 1.44
✓ Correct, FV = $2,880
3
Layer 3, finding time
$1,000 grows to exactly $2,197 at 30% p.a. compounded annually.

How many years did this take? (Hint: try small whole numbers)
FV/PV = 2.197. Check: 1.3¹ = 1.3 · 1.3² = 1.69 · 1.3³ = ?
✓ Correct, 3 years (1.30³ = 2.197)
4
Layer 4, compounding periods
An investment compounds monthly for 4 years.

How many compounding periods N are there in total?
N = m × t = 12 periods/year × 4 years
✓ Correct, N = 48 periods
5
Layer 5, larger principal
$5,000 is invested at 20% p.a. compounded annually for 2 years.

Find the future value (to the nearest dollar).
FV = 5,000 × (1.20)² = 5,000 × 1.44
✓ Correct, FV = $7,200
6
Layer 6, total interest earned
The final override code is the interest earned, not the future value.

$4,000 is invested at 10% p.a. compounded annually for 3 years.

What is the total interest earned (FV minus principal)?
FV = 4,000 × (1.10)³ = 4,000 × 1.331 = $5,324. Interest = FV − PV.
✓ Correct, Interest = $1,324

💜 VAULT UNLOCKED

All six security layers cleared. The vault door swings open, the analyst steps out, data drive in hand. Market closed, analyst safe.

FV = PV × (1+r)ⁿ
FV = PV × (1+r/m)^(mt)
Interest = FV − PV
N = m × t
EAR = (1+r/m)^m − 1
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