To calculate the total costs of buying and leasing the motor vehicle, let's break it down step by step.

1. Cost of Buying:

• Down payment: $1,700

• Loan payments: $440 per month for 36 months.

  Total loan payments = $440 \times 36 = 15,840$

• Estimated value at end of loan: $5,800 (this is the residual value of the vehicle, which reduces the total cost of ownership)

  However, we need to account for the opportunity cost of tying up money in the down payment and loan payments. To do this, we apply the opportunity cost interest rate of 8%.

Formula to calculate opportunity cost on loan payments:

The opportunity cost of money that could have been invested elsewhere can be estimated using the future value formula for the down payment and monthly loan payments.

• Down payment opportunity cost:

  The future value of the down payment (FV) can be calculated as: $FV = PV \times (1 + r)^t$ where:

  • $PV$ = $1,700 (initial down payment),
  • $r$ = 0.08 (annual interest rate),
  • $t$ = 3 years (duration of the loan).

  $FV_{down\ payment} = 1,700 \times (1 + 0.08)^3 = 1,700 \times 1.259712 = 2,141.51$ The opportunity cost here is $2,141.51 - 1,700 = 441.51$.

• Loan payment opportunity cost:

  Since these are monthly payments, we'll use the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$ where:

  • $P$ = $440 (monthly loan payment),
  • $r = \frac{0.08}{12} = 0.00667$ (monthly interest rate),
  • $n = 36$ months (number of payments).

  Plugging in the values: $FV = 440 \times \frac{(1 + 0.00667)^{36} - 1}{0.00667} = 440 \times \frac{1.26824 - 1}{0.00667} = 440 \times 40.246 = 17,708.24$ The opportunity cost here is $17,708.24 - 15,840 = 1,868.24$.

• Total opportunity cost for buying: $441.51 + 1,868.24 = 2,309.75$

Now, subtract the residual value of the vehicle from the total cost:

$\text{Total cost of buying} = (1,700 + 15,840 + 2,309.75) - 5,800 = 19,849.75 - 5,800 = 14,049.75$

2. Cost of Leasing:

• Security deposit: $890

• Lease payments: $550 per month for 36 months.

  Total lease payments = $550 \times 36 = 19,800$

• End of lease charges: $870

Adding these together:

$\text{Total cost of leasing} = 890 + 19,800 + 870 = 21,560$

3. Final Comparison:

• Cost of buying: $14,049.75
• Cost of leasing: $21,560

Therefore, buying the vehicle is more cost-effective than leasing by a difference of:

$21,560 - 14,049.75 = 7,510.25$

Conclusion:

Buying the vehicle would cost approximately $14,049.75, while leasing it would cost about $21,560 over the 36-month period. Thus, buying would save you $7,510.25 compared to leasing.

Would you like more details on any part of this calculation?

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Here are 5 related questions:

1. How would the comparison change if the interest rate were higher?
2. What is the impact of a lower residual value on the cost of buying?
3. How does increasing the lease term affect the overall cost of leasing?
4. What is the effect of a down payment on the total cost of buying?
5. How can depreciation rates influence the decision to buy versus lease?

Tip: When deciding between buying and leasing, always consider factors like the residual value and opportunity cost of your funds to get a clearer financial picture.