Question

(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?

Answer 1

The formula for the simple interest compound is

`A=P\cdot(1+rt)`

in which time is given in years.

then, the simple interest is

`\begin{gathered} A=60000\cdot(1+0.1\cdot1) \\ A=60000\cdot(1.1) \\ A=66000 \end{gathered}`

the compounded interest formula is

`A=P\cdot(1+(r)/(n))^(nt)`

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

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

then the difference between the compound and the simple interest is

`66150-66000=150`