DSC1630 Assignment 2 Semester 1 2026 Due 25 March 2026

DSC1630
Assignment 2
Semester 1
Due 25 March 2026

,Question 1
Q: How much remains in the first account two years after the withdrawal?

A:
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
Q: How long was R1 000 invested to grow to R1 605 at 11% simple interest?

A:

1605 = 1000 (1 + 0.11𝑡) 𝑡 = 0.605/0.11 = 5.50

Final Answer: 5.50 years

, Question 3
Q: What nominal rate compounded weekly gives an effective rate of 29.61%?

A:

(1 + 𝑟/52)52 = 1.2961

Weekly rate:

(1.2961)1/52 − 1 = 0.00499

Nominal rate:

52 × 0.00499 = 0.2595

Final Answer: 25.95% nominal p.a.




Question 4
Q: How long does R20 000 take to grow to R45 200 at 12% simple interest?

A:

45200 = 20000 (1 + 0.12𝑡) 𝑡 = 1.26/0.12 = 10.5

Final Answer: 10.5 years