Question

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.

Answer 1

Hello

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

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

Let's solve for p

`\begin{gathered} a=p(1+(r)/(n))^(nt) \\ 300000=p(1+(0.08)/(2))^(2*17) \\ 300000=p(1+0.04)^(34) \\ 300000=p(1.04)^(34) \\ 300000=p*3.794 \\ p=(300000)/(3.794) \\ p=79072.2 \end{gathered}`

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