For a initial amount P, the total accumulated T after t semesters with a interest rate r, which is compounded semi-annually, is given by the formula:
[tex]T=P\cdot(1+r)^t[/tex]Then, the interest rate is given by:
[tex]\begin{gathered} P\cdot(1+r)^t=T \\ (1+r)^t=\frac{T}{P} \\ 1+r=\sqrt[t]{\frac{T}{P}} \\ r=\sqrt[t]{\frac{T}{P}}-1 \end{gathered}[/tex]Therefore, for P = ₱30,000, T = ₱89,000 and t = 20 semesters, we have:
[tex]\begin{gathered} r=\sqrt[20]{\frac{89,000}{30,000}}-1 \\ r=\sqrt[20]{2.97}-1 \\ r=1.0559-1 \\ r=0.0559=\text{ 5.59\%} \end{gathered}[/tex]