Lecture No.13Chapter 4

Contemporary Engineering EconomicsCopyright © 2010

Contemporary Engineering Economics, 5th edition, © 2010

Debt ManagementCredit card debt and commercial loans are among the most significant financial transactions involving interest.

Contemporary Engineering Economics, 5th edition, © 2010

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

Contemporary Engineering Economics, 5th edition, © 2010

The interest payment in period n is, In= i x Bn-1 = A x (P/A, i, N-n+1) x i

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 6th payment

A = $5,000(A/P, 1%, 24) = $235.37

Contemporary Engineering Economics, 5th edition, © 2010

Contemporary Engineering Economics, 5th edition, © 2010

Example 4.13 Continued

To compute I6, we first need to find B5,

B5 = $235.37 x (P/A, 1%, 19) = $ 4,054.44

Then, I6 = $ 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,

P6 = $235.37 – 40.54 = $194.83

The remaining balance after the 6th payment, B6, is equal to $3,859.62 as computed on the previous slide.

Example 4.15 Financing your Vehicle

Contemporary Engineering Economics, 5th edition, © 2010

Home MortgageTypes of Home Mortgages The Cost of a MortgageFixed-rate mortgageAdjustable-rate mortgageHybrid Mortgage

Loan amountLoan termPayment frequencyPoints (prepaid interest)FeesTypes of mortgages

Contemporary Engineering Economics, 5th edition, © 2010

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:

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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

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