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Mastering Loan Amortization: Simplifying Payment Calculations

Understand the process of loan repayment through amortization. Learn how to calculate monthly payments, interest rates, and unpaid balances. Get insights into loan reduction strategies and formulas.

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Mastering Loan Amortization: Simplifying Payment Calculations

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  1. Chapter 10 Section 3 Amortization of Loans

  2. Amortization of Loans • The mathematics of paying off loans. • Amortization – The process of paying off a loan. • Decreasing annuity!!!!

  3. Definitions • Unpaid Balance / Principal: • Remaining amount of money that needs to be paid off. • Payment (i.e. Rent): • Amount of money paid for each compounding period (R). • Interest : • Amount of money paid to the institution loaning the money. (Based on the unpaid balance). • Applied to Principal : • Amount deducted from unpaid balance / principal.

  4. An Important Payment Formula Payment Amount = Amount for Interest + Amount Applied to Principal. Where Amount for Interest = i·(current balance) and i = r / m

  5. Example • Given • Place $20,000 down on a $120,000 house. • 30 year mortgage w/ monthly payments. • 9% interest compounded monthly. • Find the mortgage payment each month!

  6. Example Formula Solution (slide 1) • Loan = 120,000 – 20,000 = 100,000 • The formula 1 – (1 + i )– n P = ·R i • i = r/m = 0.09/12 = 0.0075 • n = (30)(12) = 360 • P =100000 • So 1 – (1 + 0.0075 )– 360 100000 = ·R 0.0075

  7. Exercise 15 Formula Solution (slide 2) 0.9321139926 100000 = ·R 0.0075 100000 = 124.2818657 ·R R = 804.6226168 The monthly payments are $804.62.

  8. Example TVM Solver Solution • Loan = 120,000 – 20,000 = 100,000 • TVM Solver: N = 360 I% = 9 PV = 100000 PMT = – 804.62 FV = 0 P/Y = C/Y = 12 Payments are $804.62 per month

  9. Example • $180,000 loan for 30 years. 5.25% interest compounded monthly. • Using TVM Solver, you can find the PMT = – 993.966666 • You MUST have the following entered in the TVM Solver: N = 360 PMT = – 993.97 I% = 5.25 FV = 0 PV = 180000 P/Y = C/Y = 12

  10. Questions about Balances • Find the balance after: • 10 years: bal( 120 ) = 147,506.38 • 21 years: bal( 21 · 12 ) = bal( 252 ) = 85, 403.60 • 25 years: bal( 25 ·12 ) = bal( 300 ) = 52,350.59

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