Problem: Mr$.$ Nia is planning to create a fund by depositing P$4,520$ every quarter for $8$ years in BPI bank that promises to pay a fixed rate over the entire term. If the amount at the end of the term is P$160,000,$ find the rate converted quarterly.

Given:

S $=160,000$

t $=8$ years

n $=4$

R $=4,520$

r $=?$