After reading the answers posted I decided to answer this question myself. I originally posted it because I thought it was an interesting little problem. I was hoping to see someone run with the numbers and blow me away by taking into account the time-value of money and the value earned by investing into an appreciating asset rather than a depreciating one. It would have been small, but would have loved to have seen the process.
The standard mortgage calculation used in the United States (see: Wikipedia) provide a reasonable guide to the lifetime of the loan. The calculations are laborious, but the
pmt function in Excel makes this easier. Given:
- Principal = $400,000.00
- Interest rate = 4%
- Periods = 360 (12 months per year for 30 years)
- Rate = 0.25% (4% / 12 months)
pmt(0.25%, 360, $400,000.00) = $1.686.42. In other words: the mandatory repayments for my loan are $1.686.42 per month for 30 years.
Using this number and building a spreadsheet to calculate the amount owing, I calculated that, with additional repayments, I will repay the loan in 8 years. At the end of the 96th month, I will owe $586.00. The spreadsheet indicates that the original
pmt calculated repayments were correct, and a loan repayment calculator from my bank indicates that 8 years is accurate, accounting for additional repayments.
However, If I subtract $1,500.00 from the additional repayment I make in my first month then I will owe $2,487.00 at the end of the 96th month. Alternatively, if I subtract $250.00 from my first additional payment, and then $170 for the 11 months immediately following that (totaling $2,080.00), I will owe $3,238.00 in the 96th month.
Therefore, by my calculations:
- the total cost of the $1,500.00 laptop is
$2,487.00 - $586.00 = $1,901.00
- the total cost of the $2,000.00 laptop is
$3,238.00 - $586.00 = $2,652.00
In summary: if the laptops are both fit for purpose and I have to buy one of them, then I will pay an additional ~$750.00 by buying the more expensive laptop. The opportunity cost of not buying the second hand laptop is $250.00, since I'm already willing to pay the $500.00 difference. Although this savings is significant, it is inconsequential in the wider scheme of things. If I miss the opportunity to purchase the cheaper laptop then the more expensive one is acceptable (value judgement).