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Amortization Schedule - Sample Problem Brittany plans to borrow $450,000 to buy a condo. She will repay the loan with level payments over a 20 year period beginning one month after the loan is made. To seal the deal, she received an inducement from the builder in which it will pay her first 3 years of loan interest. The nominal interest rate on the loan is 6% compounded monthly a.) How much is the value of the inducement? b.) How much will Brittany pay over the first 3 years?

Loan Default - Sample Problem Gringotts is considering a 2-year loan of $1,000 to a particular risk class of borrowers (in this case, wizards) and wishes to earn a minimum 8% return on the overall loan portfolio for the wizard class. In a group of 100 wizards, on average 2 will default on the loan at the end of year 1, and 3 will default at the end of year 2. Determine the interest rate that the lender must charge in order to meet its target ROR, assuming no recovery.

Loan Amortization Table Relationships (HW Problem 3.2.11) A loan is being repaid with level payments of K every 6 months. The outstanding balances on 3 consecutive payment dates are 5190.72, 5084.68, and 4973.66. Find K.

Loan Amortization Table Relationships (HW Problem 3.2.7S) lgey borrows X for 10 years at an effective annual rate of 6%. If he pays the principal and accumulated interest in one lump sum at the end of 10 years, he would pay 356.54 more in interest than if he repaid the loan with 10 level payments at the end of each year. Find X.

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Answer #1

Answer;

Problem 1

For given principal P=$450,000

Time n=20*12=240 months

Interest rate r=65/12=0.5% per month

Monthly Payment =P*r/(1-(1+r)^-n)=450000*0.5%/(1-(1+0.5%)^-240)=$3223.94

A)

Month Principle interest principle Principle Paid Principle outstanding
1 450000 2250 3223.94 973.94 449026.06
2 449026.06 2245.1303 3223.94 978.8097 448047.2503
3 448047.2503 2240.236252 3223.94 983.7037485 447063.5466
4 447063.5466 2235.317733 3223.94 988.6222672 446074.9243
5 446074.9243 2230.374621 3223.94 993.5653786 445081.3589
6 445081.3589 2225.406795 3223.94 998.5332055 444082.8257
7 444082.8257 2220.414129 3223.94 1003.525871 443079.2998
8 443079.2998 2215.396499 3223.94 1008.543501 442070.7563
9 442070.7563 2210.353782 3223.94 1013.586218 441057.1701
10 441057.1701 2205.285851 3223.94 1018.654149 440038.516
11 440038.516 2200.19258 3223.94 1023.74742 439014.7685
12 439014.7685 2195.073843 3223.94 1028.866157 437985.9024
13 437985.9024 2189.929512 3223.94 1034.010488 436951.8919
14 436951.8919 2184.759459 3223.94 1039.180541 435912.7114
15 435912.7114 2179.563557 3223.94 1044.376443 434868.3349
16 434868.3349 2174.341675 3223.94 1049.598325 433818.7366
17 433818.7366 2169.093683 3223.94 1054.846317 432763.8903
18 432763.8903 2163.819451 3223.94 1060.120549 431703.7697
19 431703.7697 2158.518849 3223.94 1065.421151 430638.3486
20 430638.3486 2153.191743 3223.94 1070.748257 429567.6003
21 429567.6003 2147.838002 3223.94 1076.101998 428491.4983
22 428491.4983 2142.457492 3223.94 1081.482508 427410.0158
23 427410.0158 2137.050079 3223.94 1086.889921 426323.1259
24 426323.1259 2131.615629 3223.94 1092.324371 425230.8015
25 425230.8015 2126.154008 3223.94 1097.785992 424133.0155
26 424133.0155 2120.665078 3223.94 1103.274922 423029.7406
27 423029.7406 2115.148703 3223.94 1108.791297 421920.9493
28 421920.9493 2109.604747 3223.94 1114.335253 420806.614
29 420806.614 2104.03307 3223.94 1119.90693 419686.7071
30 419686.7071 2098.433536 3223.94 1125.506464 418561.2007
31 418561.2007 2092.806003 3223.94 1131.133997 417430.0667
32 417430.0667 2087.150333 3223.94 1136.789667 416293.277
33 416293.277 2081.466385 3223.94 1142.473615 415150.8034
34 415150.8034 2075.754017 3223.94 1148.185983 414002.6174
35 414002.6174 2070.013087 3223.94 1153.926913 412848.6905
36 412848.6905 2064.243452 3223.94 1159.696548 411688.9939

Principle outstanding at end of 36 months = $411688.99

So value of inducement = sum of interest paid till 36 months=$77750.833

B)

Brittney pay for 3 years =36*3223.94-77750.883=$38311.00

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