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Chapter 10 Section 3 Amortization of Loans

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

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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.

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

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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!

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

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

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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

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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 = 360PMT = – 993.97 I% = 5.25FV = 0 PV = 180000P/Y = C/Y = 12

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Questions about Balances Find the balance after: 1.10 years:bal( 120 ) = 147,506.38 2.21 years:bal( 21 · 12 ) = bal( 252 ) = 85, 403.60 3.25 years:bal( 25 ·12 ) = bal( 300 ) = 52,350.59

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Chapter 3 Mathematics of Finance

Chapter 3 Mathematics of Finance

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