# 3.3 Amortization - Solutions(1)

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## 3.3 Amortization - Solutions(1)

- Pages:
- 6
- School:
- University of Texas at Austin
- Course:
- Fin 320f - Foundations of Finance

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FIN 320F Foundations of Finance 3.3 Amortization – Solutions 1. You are buying a $200,000 house. You will make a down-payment equal to 20% of the purchase price (that is, $40,000), and will borrow the remaining $160,000. You will be using a 30-year fixed rate mortgage. You have an excellent credit rating, so your lender said you qualified for a rate of 3.82%. (According to bankrate.com, this was the average rate for a 30- year fixed rate mortgage in the US as of Apr 9, 2015). Fill in the first three rows of the amortization schedule for this loan. The solution shown below was developed in Excel. Double-click on the spreadsheet to see the entire amortization table. The first row is worked out in detail under the Excel table. i. Determine the beginning balance = PVA = $160,000 ii. Determine the monthly payment N = 30 × 12 I% = 3.82 ÷ 12 PV = 160000 FV = 0 PM T = AL PH A EN TE R = -747.35 iii. Determine the interest payment = Beginning balance × (r ÷ m) = $160,000.00 × (.0382 ÷ 12) = $509.33 iv. Determine the principal payment = PMT – Interest = $747.35 – $509.33 = $238.02 v. Determine the ending balance (two different methods are shown below) = Beginning balance – Principal = $160,000.00 – $238.02 SourceDocument.docx Page 1 of 6 ©HToprac 2015-2022 $747.35 PMT 214.088473 $160,000 PMT 12 .0382 12 30 12 .0382 1 1 - 1 $160,000 PMT FIN 320F Foundations of Finance 3.3 Amortization – Solutions = $159,761.98 = Beginning balance + Interest – PMT = $160,000.00 + $509.33 – $747.35 = $159,761.98 2. Let’s say you decide to use a 15-year fixed rate mortgage instead of a 30-year mortgage. Your lender quoted you a rate 3.04%. (Again, according to bankrate.com, this was the average rate for a 15-year fixed rate mortgage in the US as of Apr 9, 2015). Fill in the first three rows of the amortization schedule. How does this second schedule differ from the first schedule? i. Determine the beginning balance = PVA = $160,000 ii. Determine the monthly payment N = 15 × 12 I% = 3.04 ÷ 12 PV = 160000 FV = 0 PM T = AL PH A EN TE R = -1108.01 iii. Determine the interest payment = Beginning balance × (r ÷ m) = $160,000.00 × (.0304 ÷ 12) = $405.33 iv. Determine the principal payment = PMT – Interest = $1,108.01 – $405.33 = $702.68 v. Determine the ending balance (two different methods are shown below) = Beginning balance – Principal = $160,000.00 – $702.68 SourceDocument.docx Page 2 of 6 ©HToprac 2015-2022 $1,108.01 PMT 144.402862 $160,000 PMT 12 .0304 12 15 12 .0304 1 1 - 1 $160,000 PMT ...

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