## Math Problem Statement

Purchase Costs Down payment $ 1,700 Loan payment $ 440 for 36 months Estimated value at end of loan $ 5,800 Opportunity cost interest rate 8 percent Leasing Costs Security deposit $ 890 Lease payment $ 550 for 36 months End of lease charges $ 870 Based on the costs listed in the table above, calculate the costs of buying and of leasing a motor vehicle.

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Finance

Opportunity Cost

Future Value of Annuity

Loan Amortization

### Formulas

Future Value (FV) = PV * (1 + r)^t

Future Value of Annuity = P * [(1 + r)^n - 1] / r

Total cost of ownership = Down payment + Loan payments + Opportunity cost - Residual value

### Theorems

Future Value Theorem

Annuity Formula

### Suitable Grade Level

College Level - Finance/Business