DSC1630 Assignment 2 (100% COMPLETE ANSWERS) Semester 2 2025

, DSC1630 Assignment 2 (100% COMPLETE
ANSWERS) Semester 2 2025
Question 1 (4 marks)
Find the equivalent nominal annual rate compounded weekly
(to 2 d.p.) for 14.90% p.a. compounded quarterly.
Step 1 — quarterly rate:
iq=0.14904=0.03725i_{q}=\dfrac{0.1490}{4}=0.03725iq
=40.1490=0.03725 (3.725% per quarter).
Step 2 — effective annual rate from quarterly compounding:
(1+iq)4−1=(1+0.03725)4−1=0.1575340471≈15.7534% (effective
annual)(1+i_q)^4-1=(1+0.03725)^4-1=0.1575340471\
approx15.7534\% \text{ (effective annual)}(1+iq
)4−1=(1+0.03725)4−1=0.1575340471≈15.7534% (effective annu
al)
Step 3 — find nominal annual rate compounded weekly (52
weeks) that gives the same effective annual rate:
We want (1+rw52)52=1+0.1575340471 (1+\dfrac{r_{w}}
{52})^{52}=1+0.1575340471(1+52rw)52=1+0.1575340471.
So
rw=52[(1+0.1575340471)1/52−1]=0.146497896…r_w = 52\
left[(1+0.1575340471)^{1/52}-1\right]=0.146497896\ldotsrw
=52[(1+0.1575340471)1/52−1]=0.146497896…