# Geometric Progressions in Finance: Loans & Depreciation
> Learn how to apply geometric progression to real-world finance, including loan repayment schemes, asset depreciation, and business decision-making.

Tags: financial-mathematics, loan-repayment, depreciation, geometric-progression, business-finance, math-education
## Practical Financial Applications of Geometric Progression
* Overview of focusing on loan repayments, depreciation, and business decision-making.

## Loan Repayments: Equal Monthly Payments
* Example: KCL Ltd borrows £331,000 for 3 months at 10% interest/month.
* Calculation: Monthly payment (x) = £133,100.
* Total repaid: £399,300.
* Application of geometric series sum in the denominator of the formula.

## Loan Repayments: Differentiated Payments
* Scheme 2: Debt reduces by an equal amount (£110,333.33) each month.
* Total repaid: £397,200.
* Comparison: The differentiated scheme is cheaper than the equal payment scheme by £2,100.

## Depreciation Calculations
* Example: A machine costing £50,000 loses 15% value annually.
* Formula: $V_n = V_0 \times (0.85)^n$.
* Value after 3 years: £30,706.25.
* Use cases: Asset valuation, budgeting, and replacement planning.

## Key Takeaways
* Geometric progression models repeated percentage changes.
* Financial models use compounding for loans and repeated decline for depreciation.
* Understanding these models supports practical business and personal finance decisions.
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