Pat buys a new car for €32,000 - Leaving Cert Mathematics - Question 7 - 2020

To find this percentage, we need to determine the amount borrowed. The loan amount can be calculated as follows:

$$Amount ext{ }Borrowed = Total ext{ }Cost - Trade-in ext{ }Allowance = 32,000 - 2,000 = €30,000$$

Now, we find the percentage of the total payment relative to the borrowed amount:

Percentage = rac{Total ext{ }Payment}{Amount ext{ }Borrowed} imes 100 = rac{15,971.76}{30,000} imes 100 \\ = 53.2392 ext{ or 133.1% (to one decimal place)}

Thus, Pat repays 133.1% of the amount he borrows.

The equation for compound interest is given by:

$$(1 + r)^3 = 1.331$$

To find r, we first take the cube root of both sides:

$$1 + r = (1.331)^{1/3} \\ 1 + r ext{ (approximately)} = 1.1 \\ r = 0.1 ext{ or } 10\\%$$

Thus, the value of r is 10%.

We use the formula for depreciation, which is:

$$Value ext{ }After ext{ }3 ext{ }Years = Original ext{ }Price imes (1 - Rate)^{Years} \\ = 32,000 imes (0.8)^3 \ \ = 32,000 imes 0.512 = €16,384$$

After three years, Pat's car is valued at €16,384.

Let x be the original value of the car. The car depreciates by 20% per year, so after 3 years we can express its value as:

Value ext{ }After ext{ }3 ext{ }Years = x imes (0.8)^3 = 17,920 \\ x = rac{17,920}{(0.8)^3} \\ = rac{17,920}{0.512} \\ = €35,000

Thus, the original value of Caitlin's car was €35,000.