Given that Nelson took out a home loan that compounds interest semiannually, and the following expression represents the payable amount after t years.
150,000(1.102)^2t
which follow the formal for compound interest given by:
A=P(1+r/n)^tn
where:
A=future amount
P=principle
r=rate
n=number of terms
t=time
in our example:
1+r/n=1.012
this implies that:
r/n=0.012
number of terms=2 (it's semiannual)
thus
r/(2)=0.012
hence
r=0.012*2
r=0.024
hene
thus the answer is:
r=0.024~2.4%