Question: Tom buys a car for $12700. It depreciates by 17.5% per annum.
Work out how much it will be worth after:
3 years $ ______ [2]
5 years $ ______ [2]
7 years $ ______ [2]
10 years $ ______ [2]
Put to nearest $
1. **Problem Statement:**
Tom buys a car for $12700. It depreciates by 17.5% per year. We need to find its value after 3, 5, 7, and 10 years, rounded to the nearest dollar.
2. **Formula Used:**
The value of a depreciating asset after $t$ years is given by:
$$ V = P \times (1 - r)^t $$
where:
- $V$ is the value after $t$ years,
- $P$ is the initial price ($12700$),
- $r$ is the depreciation rate per year (17.5% = 0.175),
- $t$ is the number of years.
3. **Calculate the value after 3 years:**
$$ V = 12700 \times (1 - 0.175)^3 = 12700 \times 0.825^3 $$
Calculate $0.825^3$:
$$ 0.825^3 = 0.561515625 $$
So,
$$ V = 12700 \times 0.561515625 = 7131.25 $$
Rounded to nearest dollar:
$$ \boxed{7131} $$
4. **Calculate the value after 5 years:**
$$ V = 12700 \times 0.825^5 $$
Calculate $0.825^5$:
$$ 0.825^5 = 0.3814697266 $$
So,
$$ V = 12700 \times 0.3814697266 = 4842.66 $$
Rounded to nearest dollar:
$$ \boxed{4843} $$
5. **Calculate the value after 7 years:**
$$ V = 12700 \times 0.825^7 $$
Calculate $0.825^7$:
$$ 0.825^7 = 0.258740858 $$
So,
$$ V = 12700 \times 0.258740858 = 3286.46 $$
Rounded to nearest dollar:
$$ \boxed{3286} $$
6. **Calculate the value after 10 years:**
$$ V = 12700 \times 0.825^{10} $$
Calculate $0.825^{10}$:
$$ 0.825^{10} = 0.146977 $$
So,
$$ V = 12700 \times 0.146977 = 1866.41 $$
Rounded to nearest dollar:
$$ \boxed{1866} $$
**Final answers:**
- After 3 years: $7131$
- After 5 years: $4843$
- After 7 years: $3286$
- After 10 years: $1866$