Respuesta :
The cash price of the bike is
[tex]\text{ \$2000}[/tex]Step 1: Calculate the hire purchase downpayment
The hire purchase price (down payment) is 25% of the cash price
[tex]\begin{gathered} =25\text{ \% of \$2000} \\ =\frac{25}{100}\times2000 \\ =\text{ \$500} \end{gathered}[/tex]Step 2:Calculate the total money paid for the 10 monthly installments
The total money for the installments will be calculated as
[tex]\text{Total installments= amount of each installments }\times\text{ number of months}[/tex]Where,
[tex]\begin{gathered} \text{amount of each installments = \$250} \\ \text{Number of months = 10 } \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \text{Total installments= amount of each installments }\times\text{ number of months} \\ \text{Total installments}=\text{ \$250}\times10 \\ \text{Total installments}=\text{ \$2,500} \end{gathered}[/tex]Step 3: Calculate the Hire purchase price
The hire purchase price will be calculated using the formula below
[tex]\text{Hire purchase = }Down\text{ payments + total installements}[/tex]By substituting the values above in the formula, we will have
[tex]\begin{gathered} \text{Hire purchase = }Down\text{ payments + total installements} \\ \text{Hire purchase price= \$500 + \$2500} \\ \text{Hire purchase price}=\text{ \$3,000} \end{gathered}[/tex]Step 4: Calculate the interest by paying using hire purchase
[tex]\text{Interest = Hire purchase price - }cash\text{ price}[/tex]By substituting the values,
we will have
[tex]\begin{gathered} \text{Interest = Hire purchase price - }cash\text{ price} \\ \text{Interest}=\text{ \$3,000 - \$2000} \\ \text{Interest = \$1,000} \end{gathered}[/tex]Step 5:Calculate the interest as a percent of the cash price
To calculate the interest as the percent of the cash price, we will use the formula below
[tex]Percentage\text{ interest =}\frac{\text{interest}}{\text{cash price}}\times100\text{ \%}[/tex]By substituting the values, we will have
[tex]\begin{gathered} Percentage\text{ interest =}\frac{\text{interest}}{\text{cash price}}\times100\text{ \%} \\ Percentage\text{ interest}=\frac{1000}{2000}\times100\text{ \%} \\ Percentage\text{ interest}=50\text{ \%} \end{gathered}[/tex]Hence,
The final answer is = 50%
