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Math  /  Algebra

QuestionMai Jun wants to buy the gaming laptop on hire-purchase. She pays a deposit of 20%20 \% of the cash price and the remaining will be paid in 24 monthly instalments of $134.68\$ 134.68 at a simple interest rate of r%r \% per annum. (a) Calculate the extra amount she pays compared to the cash price.  Mepsit =20100×$3848=$769.60 extra paid =$4001.92−$3848=$133.92\begin{array}{l} \text { Mepsit }=\frac{20}{100} \times \$ 3848 \\ =\$ 769.60 \\ \text { extra paid }=\$ 4001.92-\$ 3848 \\ =\$ 133.92 \end{array} 24 monthy instalmets =$134.68×24=$3232.32 Chire-prohase) =$ Total amant of movey =$3232.32+$769.60=$4001.92\begin{aligned} 24 \text { monthy instalmets } & =\$ 134.68 \times 24 \\ & =\$ 3232.32 \\ \text { Chire-prohase) } & =\$ \begin{aligned} \text { Total amant of movey } & =\$ 3232.32+\$ 769.60 \\ & =\$ 4001.92 \end{aligned} \end{aligned}
Answer \153.92 153.92 \qquad[3](b)Henceorotherwise,calculatethevalueof [3] (b) Hence or otherwise, calculate the value of r$.

Studdy Solution

STEP 1

1. The cash price of the gaming laptop is \$3848.
2. The deposit is 20% of the cash price.
3. The remaining amount is paid in 24 monthly installments of \$134.68 with a simple interest rate of \( r \%\) per annum.
4. We need to calculate the extra amount paid compared to the cash price.
5. We need to find the annual interest rate \( r \).

STEP 2

1. Calculate the deposit amount.
2. Calculate the remaining amount to be financed.
3. Determine the total amount paid through installments.
4. Calculate the total amount paid including the deposit.
5. Calculate the extra amount paid compared to the cash price.
6. Use the simple interest formula to find the interest rate r r .

STEP 3

Calculate the deposit amount, which is 20% of the cash price.
Deposit=20100×$3848=$769.60\text{Deposit} = \frac{20}{100} \times \$3848 = \$769.60

STEP 4

Calculate the remaining amount to be financed after the deposit.
Remaining amount=$3848−$769.60=$3078.40\text{Remaining amount} = \$3848 - \$769.60 = \$3078.40

STEP 5

Determine the total amount paid through monthly installments.
Total installments=24×$134.68=$3232.32\text{Total installments} = 24 \times \$134.68 = \$3232.32

STEP 6

Calculate the total amount paid including the deposit.
Total amount paid=$769.60+$3232.32=$4001.92\text{Total amount paid} = \$769.60 + \$3232.32 = \$4001.92

STEP 7

Calculate the extra amount paid compared to the cash price.
Extra amount paid=$4001.92−$3848=$153.92\text{Extra amount paid} = \$4001.92 - \$3848 = \$153.92

STEP 8

Use the simple interest formula to find the interest rate r r .
Simple interest formula: I=P×r×t I = P \times r \times t
Where: - I I is the interest paid, - P P is the principal amount (\$3078.40), - \( r \) is the annual interest rate (as a decimal), - \( t \) is the time in years (2 years).
First, calculate the total interest paid:
I=$3232.32−$3078.40=$153.92I = \$3232.32 - \$3078.40 = \$153.92
Now, solve for r r :
r=IP×t=$153.92$3078.40×2=$153.92$6156.80≈0.025r = \frac{I}{P \times t} = \frac{\$153.92}{\$3078.40 \times 2} = \frac{\$153.92}{\$6156.80} \approx 0.025
Convert the decimal to a percentage:
r≈0.025×100=2.5%r \approx 0.025 \times 100 = 2.5\%
The value of r r is approximately 2.5%.

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