DSC1630 Assignment 2 2025 Semester 2

DSC1630
ASSIGNMENT 2 SEMESTER 2 2025

UNIQUE NO.
DUE DATE: SEPTEMBER 2025

, Question 1

Problem: Determine the equivalent weekly compounded interest rate (to two decimal
places) of an interest rate of 14.90% per year, compounded quarterly.

Solution (steps):

1. Quarterly nominal rate (per quarter):

0.1490
𝑗𝑞 = = 0.03725
4

2. Find the effective annual rate (EAR) generated by 14.90% p.a. compounded
quarterly:

EAR = (1 + 𝑗𝑞 )4 − 1 = (1 + 0.03725) 4 − 1

Numerically,

EAR ≈ 0.1575340471 (i.e. 15.75340471%)

3. Let the nominal weekly rate (convert to percentage p.a., compounded weekly) be
𝑖week,nom . Weekly compounding has 52 periods per year. We require

(1 + 𝑖week,nom ⁄52)52 = 1 + EAR

So

𝑖week,nom ⁄52 = (1 + EAR)1/52 − 1

and

𝑖week,nom = 52((1 + EAR)1/52 − 1).

4. Compute:

𝑖week,nom ≈ 0.1464978960 (decimal) = 14.64978960% p.a.

Answer (rounded to two decimal places): 14.65% p.a. (nominal, compounded
weekly).