The problem describes a scenario where a computer can be purchased for N$10,500.00 in cash, or through a hire purchase agreement requiring a 10% deposit and monthly installments of 0.5% of the remaining amount plus N$250. The problem asks us to calculate: (a) the deposit amount, (b) the monthly instalment, (c) the duration of the installment plan if the total hire purchase price is N$10,849.63, and (d) the percentage difference between the amount paid and the cash price.

1. Problem Description

The problem describes a scenario where a computer can be purchased for N$10,500.00 in cash, or through a hire purchase agreement requiring a 10$

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0. The problem asks us to calculate: (a) the deposit amount, (b) the monthly instalment, (c) the duration of the installment plan if the total hire purchase price is N$10,849.63, and (d) the percentage difference between the amount paid and the cash price.

2. Solution Steps

(a) The deposit:

The deposit is 10% of the cash price, which is N$10,500.

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0. $Deposit = (10/100) * 10500 = 1050$

(b) Monthly installment:

First, we need to find the remaining amount after the deposit is paid.

$RemainingAmount = CashPrice - Deposit = 10500 - 1050 = 9450$

The monthly installment is 0.5% of the remaining amount plus N$

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0. $MonthlyInstallment = (0.5/100) * RemainingAmount + 250 = (0.005 * 9450) + 250 = 47.25 + 250 = 297.25$

(c) Duration of installment plan:

The total payment for hire purchase is N$10,849.

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3. The deposit paid is N$1,

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0. $TotalInstallmentAmount = TotalPayment - Deposit = 10849.63 - 1050 = 9799.63$

Each monthly installment is N$297.

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5. $NumberOfInstallments = TotalInstallmentAmount / MonthlyInstallment = 9799.63 / 297.25 \approx 32.96$

Since we cannot have a fraction of a month, let's consider that it is approximately 33 months.

Number of years $= 33 / 12 = 2.75$ years. So, 2 years and $0.75 \times 12 = 9$ months.

So, the installments last for 2 years and 9 months.

Note that $33 \times 297.25 = 9700+297*3 = 9819.25$ this shows that the calculation does not match exactly with the given data. Let's denote the exact number of months by n. Then $1050+ n(0.005(10500-1050)+250)=10849.63$, $1050 + n(47.25+250) = 10849.63$, $1050 + n(297.25) = 10849.63$.

Then $297.25n = 9799.63$ and $n = 9799.63 / 297.25 = 32.96 \approx 33$ months.

$33 \text{ months} = 2 \text{ years and } 9 \text{ months} = 2 \text{ years, } 9 \text{ months and } 0 \text{ weeks}$.

(d) Percentage difference between the amount paid and the cash price:

$Difference = TotalPayment - CashPrice = 10849.63 - 10500 = 349.63$

$PercentageDifference = (Difference / CashPrice) * 100 = (349.63 / 10500) * 100 \approx 3.33\%$

3. Final Answer

(a) The deposit is N$1050.

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0. (b) The monthly installment is N$297.

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5. (c) The installment lasts for 2 years, 9 months and 0 weeks.

(d) The percentage difference is 3.33%.