4. Ashley and Aileen want to accumulate ₱300,000, 17 years from now, as a college fund for their baby daughter, Aria. Calculate how much they must invest now, at an interest rate of 8% compounded semi-annually, in order to have ₱300,000 in 17 years.

Respuesta :

Hello

To solve this question, we should use the formula of compound interest and calculate the principal

[tex]\begin{gathered} A=p(1+\frac{r}{n})^{nt} \\ A=300000 \\ r=8\text{ \% = 0.08} \\ t=17 \\ n=2 \\ p=\text{ ?} \end{gathered}[/tex]

Let's solve for p

[tex]\begin{gathered} a=p(1+\frac{r}{n})^{nt} \\ 300000=p(1+\frac{0.08}{2})^{2\times17} \\ 300000=p(1+0.04)^{34} \\ 300000=p(1.04)^{34} \\ 300000=p\times3.794 \\ p=\frac{300000}{3.794} \\ p=79072.2 \end{gathered}[/tex]

From the calculation above, the principal or what they need to invest P79,072.2 now to get P300,000