Question

Ms. Cruz lent Php5000.00 each to Keen and Kyle at 15% per annum for 3 ¹/₂ years and 5 years respectively. Find the difference in the interest paid by them.

Answer 1

The simple interest formula allows us to calculate the interest earned or paid on a loan. According to this formula, the amount of interest is given by I = C · i · t, where C is the principal, i is the annual interest rate in decimal form, and t is the period of time expressed in years.

`I=C\cdot t\cdot i`

Where:

• I = interest

,

• C= initial capital

,

• t = time in years

,

• i =annual interest

From the problem we have

`\begin{gathered} C=5000 \\ i=0.15 \\ I=5000\cdot(0.15)\cdot t \\ I=750\cdot t \end{gathered}`

The loans for Keen and Kyle differ in time so we will calculate the interest of both loans

`\begin{gathered} I=750\cdot(3.5) \\ I=2625\to Keen \end{gathered}`
`\begin{gathered} I=750\cdot(5) \\ I=3750\to Kyle \end{gathered}`

To find the difference, we subtract the interest values that Keen and Kyle paid to Mrs. Cruz.

`3750-2625=1125`

Kyle will pay $1,125 more interest on the loan than Keen