, DSC1630 Assignment 1 Semester 1 2026 - DUE 13 March 2026
Question 1
Balance of first account 2 years after withdrawal.
Given:
P = R900
j = 6.5% = 0.065
m = 4 (quarterly)
t₁ = 3.5 years
Withdrawal = R1 000
t₂ = 2 years
Step A: Balance after 3.5 years
𝑗 𝑡𝑚
𝑆 = 𝑃 (1 + )
𝑚
0.065 3.5 × 4
𝑆 = 900 (1 + )
4
𝑆 = 900(1.01625)14
𝑆 ≈ 900 × 1.253139
𝑆 ≈ 1 127.83
Step B: Subtract withdrawal
New Balance = 1 127.83 − 1 000
New Balance = R127.83
Step C: Compound remaining balance for 2 more years
0.065 2 × 4
𝑆𝑓𝑖𝑛𝑎𝑙 = 127.83 (1 + )
4
𝑆𝑓𝑖𝑛𝑎𝑙 = 127.83(1.01625)8
𝑆𝑓𝑖𝑛𝑎𝑙 ≈ 127.83 × 1.137639
𝑆𝑓𝑖𝑛𝑎𝑙 ≈ 145.42
Answer: R145
Question 1
Balance of first account 2 years after withdrawal.
Given:
P = R900
j = 6.5% = 0.065
m = 4 (quarterly)
t₁ = 3.5 years
Withdrawal = R1 000
t₂ = 2 years
Step A: Balance after 3.5 years
𝑗 𝑡𝑚
𝑆 = 𝑃 (1 + )
𝑚
0.065 3.5 × 4
𝑆 = 900 (1 + )
4
𝑆 = 900(1.01625)14
𝑆 ≈ 900 × 1.253139
𝑆 ≈ 1 127.83
Step B: Subtract withdrawal
New Balance = 1 127.83 − 1 000
New Balance = R127.83
Step C: Compound remaining balance for 2 more years
0.065 2 × 4
𝑆𝑓𝑖𝑛𝑎𝑙 = 127.83 (1 + )
4
𝑆𝑓𝑖𝑛𝑎𝑙 = 127.83(1.01625)8
𝑆𝑓𝑖𝑛𝑎𝑙 ≈ 127.83 × 1.137639
𝑆𝑓𝑖𝑛𝑎𝑙 ≈ 145.42
Answer: R145
