Question

Clair Walsh wishes to purchase​ a(n) $630,000 house. She has accumulated a $110,000 down​ payment, but she wishes to borrow $520,000 on a 25​-year mortgage. For​ simplicity, assume annual mortgage payments occur at the end of each year and there are no loan fees.

1.	What are Walsh's annual payments if her interest rate is​ (a) 4​%, ​(b) 6%, and​ (c) 10​%, compounded​ annually?
2.	Repeat number 1 for a 20​-year mortgage.
3.	Suppose Walsh had to choose between a 25​-year and a 20​-year mortgage, either one at​ a(n) 6​% interest rate. Compute the total payments and total interest paid on​ (a) a 25-year mortgage and​ (b) a 20​-year mortgage.

Answer 1

2 Value of the house 630,000 $ 110,000 $ 520,000 3 Ownn Fund 4 Loan Amount 5 Mortgage term 6 Interest rate 7 Annnual instalment $33,286 $ 40,678 $ 57,287 25 years 4% 10% 0 9 Value of the house 630,000 $ 110,000 $ 520,000 10 Ownn Fund 11 Loan Amount 12 Mortgage term 13 Interest rate 14 Annnual instalment $38,263 $ 45,336 20 years 4% 10% 61,079

Begining balance Interest Principle Total year payment payment paymentsbalance 1 $ 520,000$31,200 9,478 $ 40,678 510,522 2 $ 510,522$30,631 $ 10,047 $ 40,678 500,476 3 500,476 $ 30,029 10,649 40,678 489,826 4 $ 489,826 29,390 11,288 $ 40,678 478,538 5 $ 478,538 28,712 11,966 $ 40,678 466,572 6 466,572$27,994 12,684 40,678 453,889 233 $ 13,445 $ 40,678$440,444 427 14,251 40,678 426,193 9 $ 426,193$25,572 $ 15,106 $ 40,678 411,087 10 $ 411,087 $ 24,665 16,013 $ 40,678 $ 395,074 11 $ 395,074$ 23,704 16,973 40,678 $ 378,100 686 17,992 $ 40,678 360,108 13 $ 360,108 $ 21,607 $ 19,071 40,678 $ 341,037 14 $ 341,037 20,462 $ 20,216 $ 40,678 $ 320,821 15 $ 320,821 $ 19,249 $ 21,429 $ 40,678 $ 299,393 16 $ 299,393 $ 17,964 $ 22,714 $ 40,678 276,679 17 $ 276,679 16,601 $ 24,077 40,678 $ 252,601 18 $ 252,601 15,156 $ 25,522 $ 40,678 $ 227,080 19 $ 227,080$ 13,625 $ 27,053 40,678 $ 200,026 20 $ 200,026$ 12,002 $ 28,676 40,678 $ 171,350 21 $ 171,350 10,281 $ 30,397 40,678 $ 140,953 22 $ 140,953 $ 8,457 32,221 $ 40,678 $ 108,732 23 $ 108,732 6,524 34,154 40,678 $ 74,579 24 $ 74,579 $ 4,475 36,203 $ 40,678 $ 38,375 -0 8 440,444 12 $ 378,100 2,303 $ 38,375 $ 40,678 $ 496947 520000 25 $ 38,375 $

43 Begining Interest Principle Total Ending year balance payment payment payments balance 1 520,000 31,200 14,136 45,336 I $ 505,864 984 $ 45,336$490,880 45,336 $ 474,997 45 46 47 48 49 50 51 52 53 54 30,352 14,98445,336 $ 49 29,453 $ 15,883 $ 45,336 S 474,9 2 $ 505,864 3 $ 490,880 4 474,997 $28,500 16,836 45,336 458,161 5 458,161 $27,490 17,846 $ 45,336 440,314 6 440,314$ 26,419 18,917 $ 45,336 421,397 7 421,397$25,284 $ 20,052 45,336 401,345 8 401,34524,081 21,255 45,336 380,090 9 380,090$22,805 22,531 45,336 357,559 10 357,55921,454 $ 23,882 45,336 333,677 11 333,677 $ 20,021 25,315 45,336 308,361 12 308,361$ 18,502 $ 26,834 $ 45,336 281,527 13 281,527 $ 16,892 28,444 $ 45,336 253,083 14 253,083 $ 15,185 30,151 45,336 222,932 15 222,93213,376 31,960 45,336 190,972 16 190,972$ 11,458 33,878 45,336 $ 157,094 17 157,094 $ 9,426 35,910 45,336 121,184 18 121,184 $ 7,271 38,06545,336 83,119 19 $ 83,119 $ 4,987 40,349 45,336 42,770 20 42,770$2,566 42,770 45,336 56 57 58 59 60 61 62 63 64 65 Total 386719 520000

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