Question

At what nominal interest rate compounded semi-annually for 10 years will ₱30,000accumulate ₱89,000?

Answer 1

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:

`T=P\cdot(1+r)^t`

Then, the interest rate is given by:

`\begin{gathered} P\cdot(1+r)^t=T \\ (1+r)^t=(T)/(P) \\ 1+r=\sqrt[t]{(T)/(P)} \\ r=\sqrt[t]{(T)/(P)}-1 \end{gathered}`

Therefore, for P = ₱30,000, T = ₱89,000 and t = 20 semesters, we have:

`\begin{gathered} r=\sqrt[20]{(89,000)/(30,000)}-1 \\ r=\sqrt[20]{2.97}-1 \\ r=1.0559-1 \\ r=0.0559=\text{ 5.59\%} \end{gathered}`