L5 - 12.1 Amortization - Final Payment

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Jan 9, 2024

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12.1 Amortization: Final Payment
ex1 A debt of $32,000 is repaid by payments of $2,950 made at the end of every 6 months. Interest is j 4 = 12%. a) What is the number of payments needed to retire the debt? N I/Y P/Y C/Y PV PMT FV ? 12 2 4 32,000 0 2950 BGN/END 18.2…. N ≈ 19 ALWAYS ROUND N UP
ex1 A debt of $32,000 is repaid by payments of $2,950 made at the end of every 6 months. Interest is j 4 = 12%. b) What is the total cost of the debt for the first five years? = Total Paid – Principal Repaid Total Amount Paid in 5 years = = $29,500 10 x 2,950 Find OP 10 32,000 10 12 2 4 - 2,950 FV = -18,747.48 ? Still owe $18,747.48 Cost (Interest) So the amount of principal Repaid = 32,000 -18,747.48 = 13, 252.52 Total Cost of Interest for the first 5 years = total payments – total principal repaid = 29,500 - 13,252.52 = $16,247.48 -18,747.48
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ex1 A debt of $32,000 is repaid by payments of $2,950 made at the end of every 6 months. Interest is j 4 = 12%. c) Complete a partial amortization schedule showing details of the last 2 payments and totals. Remember N = 19 Period Payment Interest Paid Principal Repaid OP 17 18 19 Totals $ 2950 $ 3527.37 $ 792.18 $ 840.42 $ 214.82 $ 792.18 $ 48.24 $ 2735.18
Totals: Period Payment Interest Paid Principal Repaid OP 18 2,950.00 214.82 2,735.18 792.18 19 840.42 48.24 792.18 0 Total 53,940.42 Total PMTs = 18 x $ 2,950 + 840.42 Total Principal = $ 32,000 32,000 Total Interest = PMTs - Principal = 53,940.42 – 32,000 21,940.42
ex1 James took out a loan of $7800. He will pay the money back by making payments of $180 at the beginning of every month. If the bank is charging 9% compounded monthly, what is the size of the final payment? N I/Y P/Y C/Y PV PMT FV ? 9 12 12 7800 0 180 BGN/END P1 = P2 = BAL ≈ 53 53 –$157.76 52.1231… N ≈ 53 ALWAYS ROUND N UP The NEGATIVE BALANCE shows that James has overpaid by $157.76. Final payment = $180 – $157.76 = $22.24
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ex2 Jenny purchased a $96,000 property with a 25% down payment and end-of-quarter payments of $4000. If interest is j 12 = 9%, construct an amortization schedule for the final payment. N I/Y P/Y C/Y PV PMT FV 9 4 12 72 000 4000 BGN/END 0 N ≈ 24 Down payment = 96,000 × 0.25 = 24,000 PV = 96,000 – 24,000 = 72,000 23.3906…?
ex2 Jenny purchased a $96,000 property with a 25% down payment and end-of-quarter payments of $4000. If interest is j 12 = 9%, construct an amortization schedule for the final payment. P1 = P2 = BAL ≈ 24 24 –$2426.90 Final payment = $4000 – $2426.90 = $1573.10 Payment Number Payment PMT Interest Paid Principal Repaid Outstanding Principal (OP) $1538.23 $0 24 $34.87 $1573.10 ∑INT ≈ −$34.87 $1573.10 – $34.87 Jenny has overpaid by $2426.90. OR ∑PRIN ≈ − $3965.13 PRIN ≈ $3965.13 − $2426.90 = $1538.23
Homework Online Lesson #8 : 12.1 Online Lab 8 : # 2 Ex 12.1 p401 # 11, 23 Extra Practice : # 10, 12, 14, 22, 24, 26 (Answers : #10. $0, #12. $28.84 #14. $94.19 #22. $694,566.93 #24. $11,037.27 #26. $9352.36)
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