DSC1630 Assignment 2 (COMPLETE ANSWERS) Semester 2 2025 – DUE September 2025 ;100% trusted ,comprehensive and complete reliable solution with clear explanation

,DSC1630 Assignment 2 (COMPLETE ANSWERS) Semester
2 2025 – DUE September 2025 ;100% trusted
,comprehensive and complete reliable solution with clear
explanation


Question 1
Determine the equivalent weekly compounded interest rate (to two
decimal places) of an interest rate of
14,90% per year, compounded quarterly. [4]

Step-by-Step Solution
Step 1: Convert the nominal rate to an effective annual rate (EAR)

Given:

 Nominal annual interest rate r=14.90%r = 14.90\%r=14.90%
 Compounded quarterly → 4 times per year

We calculate the effective annual rate (EAR) using the formula:

𝐸𝐴𝑅 = (1 + 𝑟𝑛)𝑛 − 1𝐸𝐴𝑅
= \𝑙𝑒𝑓𝑡(1 + \𝑓𝑟𝑎𝑐{𝑟}{𝑛} \𝑟𝑖𝑔ℎ𝑡)^𝑛 − 1𝐸𝐴𝑅
= (1 + 𝑛𝑟)𝑛 − 1

𝑊ℎ𝑒𝑟𝑒:

,  𝑟 = 0.149𝑟 = 0.149𝑟 = 0.149
 𝑛 = 4𝑛 = 4𝑛 = 4

𝐸𝐴𝑅 = (1 + 0.1494)4 − 1 = (1 + 0.03725)4 − 1𝐸𝐴𝑅
= \𝑙𝑒𝑓𝑡(1 + \𝑓𝑟𝑎𝑐{0.149}{4} \𝑟𝑖𝑔ℎ𝑡)^4 − 1
= (1 + 0.03725)^4 − 1𝐸𝐴𝑅 = (1 + 40.149)4 − 1
= (1 + 0.03725)4 − 1 𝐸𝐴𝑅 = (1.03725)4 − 1
≈ 1.154374 − 1 = 0.154374𝐸𝐴𝑅 = (1.03725)^4 − 1
≈ 1.154374 − 1 = 0.154374𝐸𝐴𝑅 = (1.03725)4 − 1
≈ 1.154374 − 1 = 0.154374


✅ EAR ≈ 15.4374% annually



Step 2: Convert EAR to equivalent weekly rate

There are 52 weeks in a year. To find the weekly compounded rate, we
reverse the EAR formula:

1 + 𝑟𝑤𝑒𝑒𝑘𝑙𝑦 = (1 + 𝐸𝐴𝑅)1521 + 𝑟_{𝑤𝑒𝑒𝑘𝑙𝑦}
= (1 + 𝐸𝐴𝑅)^{\𝑓𝑟𝑎𝑐{1}{52}}1 + 𝑟𝑤𝑒𝑒𝑘𝑙𝑦
= (1 + 𝐸𝐴𝑅)521 1 + 𝑟𝑤𝑒𝑒𝑘𝑙𝑦 = (1.154374)152
≈ 1.0027481 + 𝑟_{𝑤𝑒𝑒𝑘𝑙𝑦}
= (1.154374)^{\𝑓𝑟𝑎𝑐{1}{52}} ≈ 1.0027481 + 𝑟𝑤𝑒𝑒𝑘𝑙𝑦
= (1.154374)521 ≈ 1.002748 𝑟𝑤𝑒𝑒𝑘𝑙𝑦 = 1.002748 − 1
= 0.002748𝑟_{𝑤𝑒𝑒𝑘𝑙𝑦} = 1.002748 − 1
= 0.002748𝑟𝑤𝑒𝑒𝑘𝑙𝑦 = 1.002748 − 1 = 0.002748


✅ Equivalent weekly interest rate ≈ 0.2748%