If we call $P$ our debt, and if $a(t) = 1+it $ is the accumulate amount and i is the interest rate, then $Pa(90/360)$ is the total amount to pay after 90 days and we have
$$ P a(90/360) - Pa(30/360) = P 0.02 $$
which implies that (90-30) i/ 360 = 0.02 and solving for the interest rate we obtain $i=0.12 $ or $12 \%$.
However, the solution key gives $12.245 \%$ as the solution. What am I doing wrong?
Lets say after $90$ days you repay $X$ monetary units and $0.98X$ ($1-0.02=0.98$) monetary units after $30$ days. The time difference is 60 days. Now we use the simple interest to calculate the advantage. The 60 days the interest rate in the case of simple interest is $\frac{60}{360}\cdot i$. Thus the equation is
$$0.98X\cdot \left(1+\frac{60}{360}\cdot i\right)=X$$
$$ 1+\frac{60}{360}\cdot i=\frac1{0.98}$$
$$ \frac{60}{360}\cdot i=\frac1{0.98}-\frac{0.98}{0.98}$$
$$i=6\cdot \frac{0.02}{0.98}=0.1224489...\approx 12.245\%$$
