A car was valued at 11000 If the car’s value continues to drop by the same percentage, what will it be worth by 2017?

Answer

Future Value of a Depreciating Car by 2017 – Step-by-Step Guide

🚗 Calculating Future Car Value with Constant Percentage Depreciation

🧠 Understanding the Problem

A car was valued at $38,000 in 2007. By 2013, its value dropped to $11,000. Assuming the depreciation continues at the same percentage rate, we aim to calculate its value by 2017.

📉 Step 1: Use the Exponential Decay Formula

V(t) = V₀ × (1 – r)^t

V(t): Value after t years
V₀: Initial value ($38,000)
r: Depreciation rate per year (decimal)
t: Time in years since 2007

🧮 Step 2: Find the Annual Depreciation Rate

From 2007 to 2013 is 6 years. We know:

11,000 = 38,000 × (1 – r)⁶

Divide both sides:

(1 – r)⁶ = 11,000 / 38,000 ≈ 0.2895

Now take the 6th root:

1 – r = (0.2895)^1/6 ≈ 0.7962

Solve for r:

r = 1 – 0.7962 = 0.2038 or 20.38% annual depreciation

📅 Step 3: Find the Value in 2017 (10 Years After 2007)

Now apply the formula:

V(10) = 38,000 × (1 – 0.2038)¹⁰ = 38,000 × (0.7962)¹⁰

Compute the result:

V(10) ≈ 38,000 × 0.1041 ≈ $3,956

💰 Therefore, the estimated value of the car in 2017 is approximately $3,956, assuming the same percentage depreciation continues.

✅ Summary

Initial Value (2007): $38,000
Value after 6 years (2013): $11,000
Annual Depreciation Rate: 20.38%
Estimated Value after 10 years (2017): $3,956

This method assumes a constant rate of depreciation, which is common in financial estimations but may vary in real markets.

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