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Chapter 10 Section 3 Amortization of Loans. The mathematics of paying off loans. Amortization – The process of paying off a loan. Decreasing annuity!!!!

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Presentation on theme: "Chapter 10 Section 3 Amortization of Loans. The mathematics of paying off loans. Amortization – The process of paying off a loan. Decreasing annuity!!!!"— Presentation transcript:

1 Chapter 10 Section 3 Amortization of Loans

2 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 ·R·R 1 – (1 + i ) – n P = i = r/m = 0.09/12 = n = (30)(12) = 360 P = So ·R·R 1 – ( ) – = i

7 Exercise 15 Formula Solution (slide 2) ·R·R = R = The monthly payments are $ = ·R

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

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

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


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