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Lecture No.13 Chapter 4 Contemporary Engineering Economics Copyright © 2010 Contemporary Engineering Economics, 5th edition, © 2010

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Debt Management Credit card debt and commercial loans are among the most significant financial transactions involving interest. Contemporary Engineering Economics, 5th edition, © 2010

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Example 4.12 Loan Balance, Principal, and Interest: Tabular Approach Given: P = $5,000, i = 12% APR, N = 24 months Find: A, and loan repayment schedule A = $5,000(A/P, 1%, 24) = $235.37 Contemporary Engineering Economics, 5th edition, © 2010

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Calculating the Remaining Loan Balance after Making the n th Payment Contemporary Engineering Economics, 5th edition, © 2010 The interest payment in period n is, I n = i x B n-1 = A x (P/A, i, N-n+1) x i

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Example 4.13 Loan Balance, Principal, and Interest: Remaining –Balance Method Given: P = $5,000, i = 12% APR, N = 24 months Find: Loan balance, principal, and interest payment for the 6 th payment A = $5,000(A/P, 1%, 24) = $235.37 Contemporary Engineering Economics, 5th edition, © 2010

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Example 4.13 Continued To compute I 6, we first need to find B 5, B 5 = $235.37 x (P/A, 1%, 19) = $ 4,054.44 Then, I 6 = $ 4,054.44 x 0,01 = $ 40,54. Note that the principal payment is the remaining part of the total monthly payment amount $235.37. Thus, P 6 = $235.37 – 40.54 = $194.83 The remaining balance after the 6 th payment, B 6, is equal to $3,859.62 as computed on the previous slide.

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Example 4.15 Financing your Vehicle Given: Three financing options, r = 4.5%, payment period = monthly, and compounding period = monthly Find: Which option? Issue: Which interest rate to use in calculating the equivalent cost of financing for each option Option A: Conventional Debt Financing: P debt = $4,500 + $736.53(P/A, 4.5%/12, 42) - $17,817(P/F, 4.5%/12, 42) = $17,847 Option B: Cash Financing: P cash = $31,020 - $17,817(P/F,4.5%/12,42) = $15,795 Option C: Lease Financing: P lease = $1,507.76 + $513.76(P/A, 4.5%/12, 42) + $395(P/F, 4.5%/12, 42) = $21,336 Contemporary Engineering Economics, 5th edition, © 2010

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Home Mortgage Types of Home Mortgages The Cost of a Mortgage Fixed-rate mortgage Adjustable-rate mortgage Hybrid Mortgage Loan amount Loan term Payment frequency Points (prepaid interest) Fees Types of mortgages Contemporary Engineering Economics, 5th edition, © 2010

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Example 4.16 An Interest-Only versus a Fully Amortized Mortgage Given: P = $200,000, APR = 6.6% or 0.55% per month, and N = 30 years Find: (a) monthly payment; (b) interest payments during the first year of ownership of the home. Option 1: A fully amortized payment option. Option 2: A five-year interest-only option. (a) Monthly payments. (b) Interest payments: Contemporary Engineering Economics, 5th edition, © 2010

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Calculating the Monthly Payments with Adjustable-Rate Mortgage (ARMs) Index – a guide that lenders use to measure interest rate changes Margin – an interest rate that represents the lender’s cost of doing business plus the profit Adjustment period – the period between potential interest rate adjustments (e.g., 3/1 means your interest rate is fixed for the first 3 years then could be adjusted every year thereafter.) Interest rate cap – a limit on the amount your interest can change (a periodic cap and a lifetime cap) Payment cap – how much your monthly payment can increase at each adjustment Contemporary Engineering Economics, 5th edition, © 2010

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Example 4.18 A 5/1 Hybrid Adjustable Mortgage Plan Given: Varying annual mortgage rates and N = 30 years Find: (a) the monthly payment; (b) the total interest payment over the 10-year ownership Monthly payments under 5/1 Hybrid mortgage Contemporary Engineering Economics, 5th edition, © 2010

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