3 Subtract the amount of the periodic payment available to reduce the principal

3 subtract the amount of the periodic payment

This preview shows page 36 - 45 out of 66 pages.

3. Subtract the amount of the periodic payment available to reduce the principal from the unpaid balance at the beginning of the period , obtaining the “unpaid balance at the end of the period”. 4. Equate the unpaid balance at the end of the period to the unpaid balance at the beginning of the next period. 5. Repeat the process for subsequent periods. 36
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PROBLEM 7: Loan Amortization Schedule (Months 1 – 4) 37 ↑ You Try ↑ You Try ↑ You Try HOME LOAN AMORTIZATION SCHEDULE Loan Amount = $500,000.00 Nominal Annual Interest Rate: 6.00% Monthly Interest Rate = 0.500% Months = 360 Payment Amount (round-up) = $2,997.76 A B C D E F Month Beginning Balance Monthly Payment Interest Amount . 005*B (Round-up) Principal Reduction C – D Ending Balance B – E 1 $500,000.00 $2,997.76 $2,500.00 $497.76 $499,502.24 2 $499,502.24 $2,997.76 $2,497.52 $500.24 $499,002.00 3 $499,002.00 $2,997.76 4 $2,997.76 ↑ You Try Check answers to problems Appear at the end of this document.
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38 PROBLEM 8: Loan Amortization Schedule (Months 358 – 360) HOME LOAN AMORTIZATION SCHEDULE Loan Amount = $500,000.00 Nominal Annual Interest Rate: 6.00% Monthly Interest Rate = 0.500% Months = 360 Payment Amount (round-up) = $2,997.76 A B C D E F Month Beginning Balance Monthly Payment Interest Amount . 005*B (Round-up) Principal Reduction C – D Ending Balance B – E - - - - - - - - - - - - - - - - - - 358 $8,901.60 $2,997.76 $44.51 $2,953.25 $5,948.35 359 $5,948.35 $2,997.76 360 1 4 2 3 0 ↑ You Try ↑ You Try ↑ You Try ↑ You Try Check answers to problems Appear at the end of this document.
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The Effective Annual Interest Rate (EAR) DEFINITION : The E ffective A nnual (Interest) R ate (EAR), associated with a nominal interest rate k nom , reports the annual interest rate (compounded one time a year) that yields the same FV as k nom , over the same length of time. 39
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The EAR Periodic Interest PERIODIC INTEREST: For a compounding frequency of m, the EAR satisfies: PV ( 1 + ) m t = PV (1 + EAR ) t which, when solved for EAR , gives: 40 EAR = ( 1 + ) m 1
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EXAMPLE: EAR Periodic Interest PROBLEM 9: Find the EAR associated with a 12% nominal interest rate compounded: a. Annually b. ( YOU TRY ) Semi-annually Answer: EAR = ( 1 + ) m 1 For a: EAR = ( 1 + ) 1 1 = .12 ( 12% ) For b ( YOU TRY ): 4 1 Check answers to problems Appear at the end of this document.
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The EAR Continuous Interest CONTINUOUS INTEREST: For a continuous annual interest rate k , the EAR satisfies: PV e k t = PV (1 + EAR) t which, when solved for EAR, gives: 42 EAR = e k 1
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EXAMPLE: EAR Continuous Interest PROBLEM 10 ( YOU TRY ): Find the EAR associated with a continuous annual interest rate of 12%? ANSWER: EAR = e k 1 43 Check answers to problems Appear at the end of this document.
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NOTES: The EAR NOTES: THE “ TRUTH IN LENDING ACT” (1969) requires that the EAR appear on all lending agreements. EAR provides a bench mark annual interest rate to which all other interest rates may be compared. A higher EAR will assure a larger accumulated amount (net any extra charges). EAR depends only on k nom (and m, for periodic interest) ----- it does not depend on PV, t or FV n .
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