*Case 1: How Fast Does Your Money Grow?*
1. Future Value (FV) = Present Value (PV) × (1 + r)^n
FV = 2000 × (1 + 0.06)^35
FV ≈ 2000 × 10.2857
FV ≈ 20,571.40
2. FV = 2000 × (1 + 0.06)^25
FV ≈ 2000 × 4.2919
FV ≈ 8,583.80
Difference = 20,571.40 – 8,583.80 ≈ 11,987.60
3. Using the rule of 72:
10% compounded annually: 72/10 ≈ 7.2 years to double
12% compounded annually: 72/12 ≈ 6 years to double
4. Using the rule of 72:
Interest Rate = 72 / Number of Years
= 72 / 10
≈ 7.2% per annum
*Case 2: Planning: The Key to Wealth*
1. Interest = Principal × Rate × Time
= 1000 × 0.0225 × 1
= 22.50
2. Abdol needs 4 × 700 = 2800 in the emergency fund.
Current balance = 1000
Amount to shift = 2800 – 1000 = 1800
3. FV = PV × (1 + r)^n
8000 = PV × (1 + 0.055)^5
PV ≈ 8000 / 1.2763
PV ≈ 6,269.11
*Case 3: Future Value/Present Value*
1. FV = PV × (1 + r)^n
= 250,000 × (1 + 0.05)^10
≈ 250,000 × 1.6289
≈ 407,225
2. Difference due to daily compounding:
= 100,000 × (1 + 0.02/365)^(365) – 100,000 × (1 + 0.02/2)^(2)
≈ 2,040.40 – 2,020.10
≈ 20.30
3. FV = PV × (1 + r)^n
= 80,000 × (1 + 0.18/12)^(12*4)
≈ 80,000 × 2.0379
≈ 163,032
This loan may not meet Seth’s goals of low risk due to the high interest rate.
4. PV = FV / (1 + r)^n
= 12,500 / (1 + 0.02/2)^(2*2)
≈ 12,500 / 1.0406
≈ 12,014.41