Question

A bike is sold for $2000 cash price. It can also be purchase on Hire purchase by making a down payment of 25% of the cash price and monthly installment of $250 for 10 months. Calculate the interest as a percent of the cash price

Answer 1

The cash price of the bike is

`\text{ \$2000}`

Step 1: Calculate the hire purchase downpayment

The hire purchase price (down payment) is 25% of the cash price

`\begin{gathered} =25\text{ \% of \$2000} \\ =(25)/(100)*2000 \\ =\text{ \$500} \end{gathered}`

Step 2:Calculate the total money paid for the 10 monthly installments

The total money for the installments will be calculated as

`\text{Total installments= amount of each installments }*\text{ number of months}`

Where,

`\begin{gathered} \text{amount of each installments = \$250} \\ \text{Number of months = 10 } \end{gathered}`

By substituting the values, we will have

`\begin{gathered} \text{Total installments= amount of each installments }*\text{ number of months} \\ \text{Total installments}=\text{ \$250}*10 \\ \text{Total installments}=\text{ \$2,500} \end{gathered}`

Step 3: Calculate the Hire purchase price

The hire purchase price will be calculated using the formula below

`\text{Hire purchase = }Down\text{ payments + total installements}`

By substituting the values above in the formula, we will have

`\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}`

Step 4: Calculate the interest by paying using hire purchase

`\text{Interest = Hire purchase price - }cash\text{ price}`

By substituting the values,

we will have

`\begin{gathered} \text{Interest = Hire purchase price - }cash\text{ price} \\ \text{Interest}=\text{ \$3,000 - \$2000} \\ \text{Interest = \$1,000} \end{gathered}`

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

`Percentage\text{ interest =}\frac{\text{interest}}{\text{cash price}}*100\text{ \%}`

By substituting the values, we will have

`\begin{gathered} Percentage\text{ interest =}\frac{\text{interest}}{\text{cash price}}*100\text{ \%} \\ Percentage\text{ interest}=(1000)/(2000)*100\text{ \%} \\ Percentage\text{ interest}=50\text{ \%} \end{gathered}`

Hence,

The final answer is = 50%