DSC1630 Assignment 2 (COMPLETE ANSWERS) Semester 2 2025 – DUE September 2025; 100% correct solutions and explanations.

, DSC1630 Assignment 2 (COMPLETE ANSWERS) Semester
2 2025 – DUE September 2025; 100% correct solutions and
explanations.
QUESTION 1

Find the equivalent weekly compounded interest rate for 14.90% p.a., compounded
quarterly.



𝑺𝒕𝒆𝒑 𝟏: 𝑰𝒏𝒕𝒆𝒓𝒑𝒓𝒆𝒕 𝒕𝒉𝒆 𝒈𝒊𝒗𝒆𝒏 𝒓𝒂𝒕𝒆

 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑡𝑒 (𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑒𝑑 𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦): 𝟏𝟒. 𝟗𝟎% = 𝟎. 𝟏𝟒𝟗𝟎.
 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 = 4.
 𝑄𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑟𝑎𝑡𝑒 = 0.1490/4 = 0.03725 = 3.725%0. = 0.03725 =
3.725\%0.1490/4 = 0.03725 = 3.725%.



𝑺𝒕𝒆𝒑 𝟐: 𝑭𝒊𝒏𝒅 𝒕𝒉𝒆 𝒆𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 𝒂𝒏𝒏𝒖𝒂𝒍 𝒓𝒂𝒕𝒆 (𝑬𝑨𝑹)

𝐸𝐴𝑅 = (1 + 𝑖𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦)4 − 1\𝑡𝑒𝑥𝑡{𝐸𝐴𝑅} = (1 + 𝑖_{\𝑡𝑒𝑥𝑡{𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦}})^{4} − 1𝐸𝐴𝑅
= (1 + 𝑖𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦)4 − 1 = (1 + 0.03725)4 − 1 = (1 + 0.03725)^{4} − 1
= (1 + 0.03725)4 − 1 = (1.03725)4 − 1 = (1.03725)^{4} − 1
= (1.03725)4 − 1

𝑁𝑜𝑤 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑠𝑡𝑒𝑝 𝑏𝑦 𝑠𝑡𝑒𝑝:

 (1.03725)2 = 1.03725 × 1.03725 = 1.076884(1.03725)^{2} = 1.03725 \
𝑡𝑖𝑚𝑒𝑠 1.03725 = 1.076884(1.03725)2 = 1.03725 × 1.03725 = 1.076884
 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝑎𝑔𝑎𝑖𝑛: 1.076884 × 1.03725 = 1.1169971.076884 \𝑡𝑖𝑚𝑒𝑠 1.03725 =
1.1169971.076884 × 1.03725 = 1.116997 (𝑡ℎ𝑖𝑟𝑑 𝑝𝑜𝑤𝑒𝑟)
 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑦 𝑎𝑔𝑎𝑖𝑛: 1.116997 × 1.03725 = 1.1584971.116997 \𝑡𝑖𝑚𝑒𝑠 1.03725 =
1.1584971.116997 × 1.03725 = 1.158497 (𝑓𝑜𝑢𝑟𝑡ℎ 𝑝𝑜𝑤𝑒𝑟)

𝐸𝐴𝑅 = 1.158497 − 1 = 0.158497 ≈ 15.85%\𝑡𝑒𝑥𝑡{𝐸𝐴𝑅} = 1.158497 − 1
= 0.158497 \𝑎𝑝𝑝𝑟𝑜𝑥 15.85\%𝐸𝐴𝑅 = 1.158497 − 1 = 0.158497 ≈ 15.85%


𝑺𝒕𝒆𝒑 𝟑: 𝑪𝒐𝒏𝒗𝒆𝒓𝒕 𝑬𝑨𝑹 𝒕𝒐 𝒘𝒆𝒆𝒌𝒍𝒚 𝒄𝒐𝒎𝒑𝒐𝒖𝒏𝒅𝒆𝒅 𝒓𝒂𝒕𝒆

𝑇ℎ𝑒𝑟𝑒 𝑎𝑟𝑒 𝟓𝟐 𝒘𝒆𝒆𝒌𝒔 𝒑𝒆𝒓 𝒚𝒆𝒂𝒓.
𝐼𝑓 𝑟𝑤𝑟_𝑤𝑟𝑤 𝑖𝑠 𝑡ℎ𝑒 𝑤𝑒𝑒𝑘𝑙𝑦 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑒𝑑 𝑟𝑎𝑡𝑒, 𝑡ℎ𝑒𝑛: