DSC1630
Assignment 2
Semester 1
Due 25 March 2026
,Question 1
How much remains in the first account two years after the withdrawal?
Quarterly rate:
𝑖 = 0.065/4 = 0.01625
After 3.5 years (14 quarters):
𝐴 = 900 (1.01625)14 = 1127.70
After withdrawing R1000:
1127.70 − 1000 = 127.70
Grow remaining for 2 years (8 quarters):
𝐴 = 127.70 (1.01625)8 = 145.23
Final Answer: R145
Question 2
How long was R1 000 invested to grow to R1 605 at 11% simple interest?
0.605
1605 = 1000 (1 + 0.11𝑡) 𝑡 = 0.11
= 5.50
Final Answer: 5.50 years
, Question 3
What nominal rate compounded weekly gives an effective rate of 29.61%?
(1 + 𝑟/52)52 = 1.2961 (1.2961)1/52 − 1 = 0.00499 𝑟 = 52 × 0.00499 = 0.2595
Final Answer: 25.95% nominal p.a.
Question 4
How long does R20 000 take to grow to R45 200 at 12% simple interest?
1.26
45200 = 20000 (1 + 0.12𝑡) 𝑡 = 0.12
= 10.5
Final Answer: 10.5 years
Assignment 2
Semester 1
Due 25 March 2026
,Question 1
How much remains in the first account two years after the withdrawal?
Quarterly rate:
𝑖 = 0.065/4 = 0.01625
After 3.5 years (14 quarters):
𝐴 = 900 (1.01625)14 = 1127.70
After withdrawing R1000:
1127.70 − 1000 = 127.70
Grow remaining for 2 years (8 quarters):
𝐴 = 127.70 (1.01625)8 = 145.23
Final Answer: R145
Question 2
How long was R1 000 invested to grow to R1 605 at 11% simple interest?
0.605
1605 = 1000 (1 + 0.11𝑡) 𝑡 = 0.11
= 5.50
Final Answer: 5.50 years
, Question 3
What nominal rate compounded weekly gives an effective rate of 29.61%?
(1 + 𝑟/52)52 = 1.2961 (1.2961)1/52 − 1 = 0.00499 𝑟 = 52 × 0.00499 = 0.2595
Final Answer: 25.95% nominal p.a.
Question 4
How long does R20 000 take to grow to R45 200 at 12% simple interest?
1.26
45200 = 20000 (1 + 0.12𝑡) 𝑡 = 0.12
= 10.5
Final Answer: 10.5 years
