Given:
The final amount is given as A = ₱5,000.
The number of yeats is T = 6.
The interest is compounded at the end of each 3 months, n = 4 per year.
The rate of interest is r = 8% = 0.08.
The objective is to find the amount deposited at the beginning.
Explanation:
The general formula to find the compound interest is,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt}_{} \\ P=\frac{A}{(1+\frac{r}{n})^{nt}_{}}\text{ . . . . . . . (1)} \end{gathered}[/tex]On plugging the given values in equation (1),
[tex]\begin{gathered} P=\frac{5000}{(1+\frac{0.08}{4})^{4(6)}} \\ P=\frac{5000}{(1+0.02)^{24}} \\ P=\frac{5000}{(1.02)^{24}} \\ P=3108.607439\ldots\text{..} \\ P\approx3108.61 \end{gathered}[/tex]Hence, the amount to be deposited is ₱3108.61.
