Thabo bought a new car. After three years the car is worth R70000. If the depreciation rate is 17% per annum, find the initial value of the car. Round to the nearest whole number

To find the initial value of the car, we can use the formula for depreciation:

\[
V = P \times (1 - r)^t
\]

Where:
- \( V \) is the value of the car after \( t \) years (R70,000 in this case),
- \( P \) is the initial value of the car,
- \( r \) is the annual depreciation rate (17% or 0.17),
- \( t \) is the time in years (3 years).

We need to solve for \( P \). Rearranging the formula to solve for \( P \):

\[
P = \frac{V}{(1 - r)^t}
\]

Substitute the given values:

\[
P = \frac{70000}{(1 - 0.17)^3}
\]

Now let's calculate it:

\[
P = \frac{70000}{(0.83)^3}
\]

\[
P = \frac{70000}{0.571787}
\]

\[
P \approx 122,395
\]

So, the initial value of the car was approximately **R122,395**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does changing the depreciation rate affect the initial value?
2. What would the value of the car be after 5 years at the same depreciation rate?
3. If the car depreciated at 10% per annum, what would its value be after 3 years?
4. Can you find the initial value if the car was worth R90,000 after 4 years at 17% depreciation?
5. How would the formula change if the depreciation was compounded quarterly?

**Tip:** When dealing with depreciation or any compound percentage problems, always make sure to correctly convert the percentage into a decimal before using it in calculations.

Thabo bought a new car. After three years the car is worth R70000. If the depreciation rate is 17% per annum, find the initial value of the car. Round to the nearest whole number.

Learn how to find the initial value of a car given a 17% annual depreciation rate over 3 years. This example problem illustrates key concepts in exponential decay and depreciation, suitable for students in Grades 10-12.

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