DSC1630
Assignment 1
Semester 1
Due 13 March 2026
,Question 1
Question
Hassim deposits R900 into a savings account paying 6,5% interest per year,
compounded quarterly. After three and a half years he withdraws R1 000 and leaves the
rest invested. What is the total amount in the first account two years after the
withdrawal?
Answer
Quarterly interest rate:
0.065
𝑖= = 0.01625
4
Number of quarters in 3.5 years:
𝑛 = 3.5 × 4 = 14
Amount after 3.5 years:
𝐴 = 900 (1.01625)14 = 900(1.253) = 1127.70
Amount remaining after withdrawal:
1127.70 − 1000 = 127.70
Number of quarters for the next 2 years:
𝑛=2×4=8
Accumulated value after 2 more years:
𝐴 = 127.70 (1.01625)8 = 127.70(1.1378) = 145.23
Final Answer:
𝑅145
, Question 2
Question
R1 000 is invested at 11% simple interest and grows to R1 605. Determine the time
invested.
Answer
Simple interest formula:
0.605
𝑆 = 𝑃 (1 + 𝑟𝑡) 1605 = 1000 (1 + 0.11𝑡) 1 + 0.11𝑡 = 1.605 0.11𝑡 = 0.605 𝑡 = 0.11
=
5.50 years
Final Answer:
5.50 years
Assignment 1
Semester 1
Due 13 March 2026
,Question 1
Question
Hassim deposits R900 into a savings account paying 6,5% interest per year,
compounded quarterly. After three and a half years he withdraws R1 000 and leaves the
rest invested. What is the total amount in the first account two years after the
withdrawal?
Answer
Quarterly interest rate:
0.065
𝑖= = 0.01625
4
Number of quarters in 3.5 years:
𝑛 = 3.5 × 4 = 14
Amount after 3.5 years:
𝐴 = 900 (1.01625)14 = 900(1.253) = 1127.70
Amount remaining after withdrawal:
1127.70 − 1000 = 127.70
Number of quarters for the next 2 years:
𝑛=2×4=8
Accumulated value after 2 more years:
𝐴 = 127.70 (1.01625)8 = 127.70(1.1378) = 145.23
Final Answer:
𝑅145
, Question 2
Question
R1 000 is invested at 11% simple interest and grows to R1 605. Determine the time
invested.
Answer
Simple interest formula:
0.605
𝑆 = 𝑃 (1 + 𝑟𝑡) 1605 = 1000 (1 + 0.11𝑡) 1 + 0.11𝑡 = 1.605 0.11𝑡 = 0.605 𝑡 = 0.11
=
5.50 years
Final Answer:
5.50 years
