Question

Ali borrowed Php22,000 for 3months at the discount rate of 5 ¼ % from a bank. Find the (a) bank’s discount and (b) proceeds.

Answer 1

If an M amount is borrowed for a time t at a discount rate of r per year, then the discount D is calculated as

`\begin{gathered} D=M\cdot r\cdot t \\ \\ \text{where} \\ r\text{ is expressed in decimals} \end{gathered}`
`\begin{gathered} \text{Given} \\ M=22000 \\ r=5(1)/(4)\%\rightarrow5.25\%\rightarrow0.0525 \\ t=\mleft((3)/(12)\mright)\text{or }0.25\text{ (3 months out of 1 year or 12 months} \end{gathered}`

Substitute the following values to get the bank's discount.

`\begin{gathered} D=Mrt \\ D=(22000)(0.0525)((3)/(12)) \\ D=288.75 \end{gathered}`

Therefore, the bank's discount is Php 288.75.

To calculate for proceeds, subtract the amount borrowed by the bank's discount.

`\begin{gathered} P=M-D \\ P=22000-288.75 \\ P=21711.25 \end{gathered}`

The proceeds given to Ali is Php 21,711.25.