Math  /  Algebra

Question15. The cash price of a new car is $87500\$ 87500. (i) Tim buys the car on hire purchase.
He pays a deposit of one-fifth of the cash price. He then makes 48 monthly payments of $1960\$ 1960. What is the total amount that Tim pays for the car? $87500÷5=$77500$1960×48=$94080 Trach =$94080+$17500=$$111580\begin{array}{l} \$ 87500 \div 5 \\ =\$ 77500 \\ \$ 1960 \times 48 \\ =\$ 94080 \\ \text { Trach }=\$ 94080+\$ 17500 \\ =\$ \$ 111580 \end{array} Answer $111580\$ 111580 [2] (ii) The original value of the car is its cash price of $87500\$ 87500.
Each year the value of the car decreases by 10%10 \% of its value at the start of the year. At the end of three years, Tim decides to sell the car. Calculate the overall percentage reduction in the value of the car compared with its original value.

Studdy Solution

STEP 1

What is this asking? We need to figure out how much Tim pays in total for his car, bought on a payment plan, and then calculate how much the car depreciates after three years. Watch out! Don't forget to add the deposit to the total cost of the monthly payments!
Also, remember that the car's value decreases by a percentage of its *current* value each year, not the original price.

STEP 2

1. Calculate the total hire purchase cost.
2. Calculate the car's value after depreciation.
3. Calculate the overall percentage reduction.

STEP 3

Alright, let's **calculate** that deposit!
Tim pays one-fifth of the cash price, which is $87500\$87500.
So, the deposit is 15$87500=$17500 \frac{1}{5} \cdot \$87500 = \$17500 .

STEP 4

Next, let's see how much Tim pays in those **monthly payments**.
He makes 48 payments of $1960\$1960 each.
So, the total amount paid through monthly payments is 48$1960=$94080 48 \cdot \$1960 = \$94080 .

STEP 5

Now, let's add those two amounts together to find the **total cost** Tim paid for the car.
That's $17500+$94080=$111580 \$17500 + \$94080 = \$111580 .
Boom!

STEP 6

The car loses 10%10\% of its value each year.
So, each year, it retains 100%10%=90%100\% - 10\% = 90\% of its value.
That means we multiply the value by 0.90.9 each year.

STEP 7

After the **first year**, the car's value is $875000.9=$78750 \$87500 \cdot 0.9 = \$78750 .

STEP 8

After the **second year**, the value is $787500.9=$70875 \$78750 \cdot 0.9 = \$70875 .

STEP 9

And after the **third year**, the value is $708750.9=$63787.50 \$70875 \cdot 0.9 = \$63787.50 .

STEP 10

The **reduction in value** is the **original value** minus the **final value**: $87500$63787.50=$23712.50 \$87500 - \$63787.50 = \$23712.50 .

STEP 11

To find the **percentage reduction**, we divide the **reduction in value** by the **original value** and multiply by 100: $23712.50$8750010027.1% \frac{\$23712.50}{\$87500} \cdot 100 \approx 27.1\% .

STEP 12

Tim paid a total of $111580\$111580 for the car through the hire purchase plan.
After three years, the car's value decreased by approximately 27.1%27.1\% compared to its original value.

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