Given -
Final Amount = $1500.00
Time Period = 2 years
Rate of interest = 4% compounded semi-annually.
To Find -
How much should she invest (Principle Amount)=?
Step-by-Step Explanation -
We know the formula for the compound interest
[tex]A\text{ = P\lparen1 + }\frac{r}{n}\text{\rparen}^{nt}[/tex]Where,
n = 2
As it is semi-annually
Now, putting the values in the formula
[tex]\begin{gathered} 1500.00\text{ = P\lparen1+ }\frac{.04}{2}\text{\rparen}^{2\times2} \\ \\ 1500.00\text{ =P\lparen1 + .02\rparen}^4 \\ \\ 1500.00\text{ = P\lparen1.02\rparen}^4 \\ \\ P\text{ = }\frac{1500.00}{1.08} \\ \\ P\text{ = 1388.88} \end{gathered}[/tex]Final Answer -
Principle Amount = $1388.88
