, DSC1630 Assignment 2 (COMPLETE ANSWERS)
Semester 1 2025 - DUE April 2025
Question 1
Determine the equivalent continuous compounding rate (to two
decimal places) of an interest rate of 17,5% per year,
compounded quarterly.
[4]
Question 1: Equivalent Continuous Compounding Rate
We are given a nominal interest rate of 17.5% per year,
compounded quarterly. The formula to convert a
nominal rate to an equivalent continuously compounded
rate is:
𝑟𝑐 = ln(1 + 𝑟𝑚) × 𝑚𝑟𝑐
= \𝑙𝑛(1 + \𝑓𝑟𝑎𝑐{𝑟}{𝑚}) × 𝑚𝑟𝑐
= ln(1 + 𝑚𝑟) × 𝑚
𝑊ℎ𝑒𝑟𝑒:
𝑟𝑐𝑟𝑐𝑟𝑐 = 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑟𝑎𝑡𝑒
𝑟 = 17.5% = 0.175𝑟 = 17.5\% = 0.175𝑟 =
17.5% = 0.175 (𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑎𝑛𝑛𝑢𝑎𝑙 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒)
𝑚 = 4𝑚 = 4𝑚 =
4 (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟)
𝑺𝒕𝒆𝒑 𝟏: 𝑪𝒐𝒎𝒑𝒖𝒕𝒆 𝒕𝒉𝒆 𝒒𝒖𝒂𝒓𝒕𝒆𝒓𝒍𝒚 𝒓𝒂𝒕𝒆
Semester 1 2025 - DUE April 2025
Question 1
Determine the equivalent continuous compounding rate (to two
decimal places) of an interest rate of 17,5% per year,
compounded quarterly.
[4]
Question 1: Equivalent Continuous Compounding Rate
We are given a nominal interest rate of 17.5% per year,
compounded quarterly. The formula to convert a
nominal rate to an equivalent continuously compounded
rate is:
𝑟𝑐 = ln(1 + 𝑟𝑚) × 𝑚𝑟𝑐
= \𝑙𝑛(1 + \𝑓𝑟𝑎𝑐{𝑟}{𝑚}) × 𝑚𝑟𝑐
= ln(1 + 𝑚𝑟) × 𝑚
𝑊ℎ𝑒𝑟𝑒:
𝑟𝑐𝑟𝑐𝑟𝑐 = 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑟𝑎𝑡𝑒
𝑟 = 17.5% = 0.175𝑟 = 17.5\% = 0.175𝑟 =
17.5% = 0.175 (𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑎𝑛𝑛𝑢𝑎𝑙 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒)
𝑚 = 4𝑚 = 4𝑚 =
4 (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑𝑠 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟)
𝑺𝒕𝒆𝒑 𝟏: 𝑪𝒐𝒎𝒑𝒖𝒕𝒆 𝒕𝒉𝒆 𝒒𝒖𝒂𝒓𝒕𝒆𝒓𝒍𝒚 𝒓𝒂𝒕𝒆
