, 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 use the formula to convert a nominal interest rate to a
co𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑟𝑎𝑡𝑒:
𝑟𝑐 = mln(1 + 𝑟𝑚) 𝑟𝑐 = 𝑚 \𝑙𝑛(1 + \𝑓𝑟𝑎𝑐{𝑟}{𝑚})𝑟𝑐
= 𝑚𝑙𝑛(1 + 𝑚𝑟)
𝑤ℎ𝑒𝑟𝑒:
𝑟 = 17.5% = 0.175𝑟 = 17.5\% = 0.175𝑟 =
17.5% = 0.175 (𝑎𝑛𝑛𝑢𝑎𝑙 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒),
𝑚 = 4𝑚 = 4𝑚 = 4 (𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔),
𝑟𝑐𝑟𝑐𝑟𝑐 𝑖𝑠 𝑡ℎ𝑒 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑟𝑎𝑡𝑒.
𝑟𝑐 = 4 ln(1 + 0.1754) 𝑟𝑐
= 4 \𝑙𝑛(1 + \𝑓𝑟𝑎𝑐{0.175}{4})𝑟𝑐
= 4 ln(1 + 40.175)
𝐿𝑒𝑡 ′ 𝑠 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒:
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 use the formula to convert a nominal interest rate to a
co𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑟𝑎𝑡𝑒:
𝑟𝑐 = mln(1 + 𝑟𝑚) 𝑟𝑐 = 𝑚 \𝑙𝑛(1 + \𝑓𝑟𝑎𝑐{𝑟}{𝑚})𝑟𝑐
= 𝑚𝑙𝑛(1 + 𝑚𝑟)
𝑤ℎ𝑒𝑟𝑒:
𝑟 = 17.5% = 0.175𝑟 = 17.5\% = 0.175𝑟 =
17.5% = 0.175 (𝑎𝑛𝑛𝑢𝑎𝑙 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒),
𝑚 = 4𝑚 = 4𝑚 = 4 (𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔),
𝑟𝑐𝑟𝑐𝑟𝑐 𝑖𝑠 𝑡ℎ𝑒 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 𝑐𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑟𝑎𝑡𝑒.
𝑟𝑐 = 4 ln(1 + 0.1754) 𝑟𝑐
= 4 \𝑙𝑛(1 + \𝑓𝑟𝑎𝑐{0.175}{4})𝑟𝑐
= 4 ln(1 + 40.175)
𝐿𝑒𝑡 ′ 𝑠 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒:
