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Chapter 10 Section 3 Amortization of Loans Chapter 10 Section 3 Amortization of Loans

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

Definitions • Unpaid Balance / Principal: – Remaining amount of money that needs to 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.

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

Example • Given • Place $20, 000 down on a $120, 000 house. • 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!

Example Formula Solution (slide 1) • Loan = 120, 000 – 20, 000 = Example Formula Solution (slide 1) • Loan = 120, 000 – 20, 000 = 100, 000 • The formula P= • • 1 – (1 + i )– n i ·R i = r/m = 0. 09/12 = 0. 0075 n = (30)(12) = 360 P =100000 So 100000 = 1 – (1 + 0. 0075 )– 360 0. 0075 ·R

Exercise 15 Formula Solution (slide 2) 100000 = 0. 9321139926 0. 0075 ·R 100000 Exercise 15 Formula Solution (slide 2) 100000 = 0. 9321139926 0. 0075 ·R 100000 = 124. 2818657 ·R R = 804. 6226168 The monthly payments are $804. 62.

Example TVM Solver Solution • Loan = 120, 000 – 20, 000 = 100, 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

Example • $180, 000 loan for 30 years. 5. 25% interest compounded monthly. • 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

Questions about Balances • Find the balance after: 1. 10 years: bal( 120 ) 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