Car Payment Is The Biggest Reason That Keeps You Poor
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How much money you can lose if you buy a 70k car now. We can do a simple math.
Make the purchase
Firstly, let’s calculate how much we lost in interest rate because of the loan.
Fees before car out of door
Assuming dealer has some fees around 1k, and sales tax 8% = 5.6k, some additional fees like warranty, window tint etc 2k. The total cost is 70k + 1k + 5.6k + 2k = 78.6k
Assuming 10k downpayment, 8% APR interest rate, 60 month payments
8% interest rate for 60-month car payments
\[P = $68,600\] \[r = \frac{0.08}{12}\] \[n = 72\]Now, let’s calculate the monthly payment:
\[r = \frac{0.08}{12} = 0.006666...\] \[M = 68600 \times \frac{0.006666... \times (1 + 0.006666...)^{72}}{(1 + 0.006666...)^{72} - 1}\] \[M = 68600 \times \frac{0.006666... \times (1.006666...)^{72}}{(1.006666...)^{72} - 1}\] \[M ≈ 68600 \times \frac{0.006666... \times 1.776129}{1.776129 - 1}\] \[M ≈ 68600 \times \frac{0.011840}{0.776129}\] \[M ≈ 68600 \times 0.015234\] \[M ≈ 1044.95\]So, with no down payment, the approximate monthly payment for a $68,600 car with an 8% APR over a 6-year term would be approximately $1,044.95, totaling $75,417.60 acoss the 6 years. With 10k downpayment, we spent $85,417.60 so far.
Car is a depreciating asset!
Secondly, let’s also take the car depreciation value into our consideration.
National average car depreciation rate
The depreciation of a car over time can vary based on factors like make, model, condition, and mileage. However, as an approximation, the national average depreciation rate for a car after 6 years is estimated to be around 50-60% of its original value.
Let’s take the midpoint of this range for our calculation, assuming a depreciation rate of 55%.
If the car’s original price is $70,000, after 6 years, its depreciated value would be:
\[Depreciated\,Value = Original\,Price \times (1 - Depreciation\,Rate)\] \[Depreciated\,Value = $70,000 \times (1 - 0.55)\] \[Depreciated\,Value = $70,000 \times 0.45\] \[Depreciated\,Value = $31,500\]Losing
Now we can know the total lost value is:
\[Total\,Lost\,Value = $85,417.60 - 31,500\] \[Total\,Lost\,Value = $54,417.60\]What if we invest instead?
Thirdly, let’s calculate how much we will lose in a very conservative investment rate with 8% in S&P 500 index fund annual return rate.
Calculation:
Future Value of Initial Investment: \(FV_{\text{initial}} = 10,000 \times (1 + \frac{0.08}{12})^{72}\)
\[FV_{\text{initial}} ≈ 10,000 \times (1.00667)^{72} ≈ 10,000 \times 1.717\] \[FV_{\text{initial}} ≈ 17,170\]Future Value of Monthly Investments: \(FV_{\text{annuity}} = 1044.95 \times \frac{(1 + \frac{0.08}{12})^{72} - 1}{\frac{0.08}{12}}\)
\[FV_{\text{annuity}} ≈ 1044.95 \times \frac{(1.00667)^{72} - 1}{0.00667} ≈ 1044.95 \times 94.506\] \[FV_{\text{annuity}} ≈ 98,978.16\]Total Future Value: \(FV_{\text{total}} = FV_{\text{initial}} + FV_{\text{annuity}}\)
\[FV_{\text{total}} ≈ 17,170 + 98,978.16\] \[FV_{\text{total}} ≈ 116,148.16\]So, the total future value is approximately $116,148.16.
Profit
The profit is $46,148.16.
The final true losing value
On a given car with 70k price tag, we are looking at
\[Difference = $54.4k + $46.1k = $100.5k\] \[Investment Rate = -$100.5k / $70k = -143%\]In other words, we are losing 100.5k truely taking the opportunity cost into consideration, that is -143% in investment return rate. If you think my math is mathing, please consider sharing to make the people around you making better financial decisions!
