Let's solve this step-by-step:
1. Determine the Hire Purchase Price:
The cash price of the motorcycle is given as [tex]$120,009. The hire purchase price is 20% more than the cash price.
\[
\text{Hire Purchase Price} = \text{Cash Price} + 20\% \times \text{Cash Price}
\]
\[
\text{Hire Purchase Price} = \$[/tex]120,009 + 0.2 \times \[tex]$120,009
\]
\[
\text{Hire Purchase Price} = \$[/tex]120,009 + \[tex]$24,001.8 = \$[/tex]144,010.8
\]
2. Calculate Total Installment Amount:
Fred makes equal monthly installments of [tex]$110,000 each. We need to calculate the total amount paid through these installments over the 8 months.
\[
\text{Total Installment Amount} = \text{Monthly Installment} \times \text{Number of Installments}
\]
\[
\text{Total Installment Amount} = \$[/tex]110,000 \times 8 = \[tex]$880,000
\]
3. Determine the Deposit:
The deposit is the difference between the hire purchase price and the total installment amount paid.
\[
\text{Deposit} = \text{Hire Purchase Price} - \text{Total Installment Amount}
\]
\[
\text{Deposit} = \$[/tex]144,010.8 - \[tex]$880,000 = -\$[/tex]735,989.2
\]
So, Fred paid a deposit of [tex]\(-\$735,989.2\)[/tex].
(Note: A negative deposit indicates there might be an issue, as typically a deposit should be a positive value, but based on the numbers given, this is the result.)
