(a) Find the simple interest on ₱60,000 for one year at 10%. (b) Find the compound interest if theinvestment is compounded semi-annually? (c) Find the difference between the compound interest and the simple interest?

Respuesta :

The formula for the simple interest compound is

[tex]A=P\cdot(1+rt)[/tex]

in which time is given in years.

then, the simple interest is

[tex]\begin{gathered} A=60000\cdot(1+0.1\cdot1) \\ A=60000\cdot(1.1) \\ A=66000 \end{gathered}[/tex]

the compounded interest formula is

[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]

In which n is the number of compounds made in 1 year, and t is given in years.

then the compounded semiannually is done 2 times per year, which leads to

[tex]\begin{gathered} A=60000\cdot(1+\frac{0.1}{2})^2 \\ A=60000\cdot(1.05)^2 \\ A=60000\cdot1.1025 \\ A=66150 \end{gathered}[/tex]

then the difference between the compound and the simple interest is

[tex]66150-66000=150[/tex]