Question

how much must be invested today in a savings account to realize Php 9.000.00 in 4 years if money earns at the rate of 4% compound quarterly​

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 9000\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}`

`9000 = P\left(1+(0.04)/(4)\right)^(4\cdot 4) \implies 9000=P(1.01)^(16) \\\\\\ \cfrac{9000}{(1.01)^(16)}=P\implies \boxed{7675.39\approx P}`