Mr. H issues a 25 year mortgage of $225,000 at an annual interest rate of 4.5% to buy a house.The mortgage payments are made annually.
1.
What is Mr. H's annual payment of principal and interest?
$17,298
$13,353
$16,691
$15,174
2.
How much interest does Mr. H pay in the second year of the mortgage?
$11,283
$9,898
$8,710
$10,888
3.
Suppose that immediately after making the second annual payment, Mr. H has the opportunity to refinance the remaining mortgage balance at an annual rate of 3.5% for the remaining period of 23 years. What is the largest lump sum refinancing payment that he would be willing to make today to secure the lower cost financing? Assume that he continues to make annual payments on the new mortgage.
$22,345
$24,580
$19,664
$25,474
4.
Using the information from the refinancing question and assuming that Mr. H refinanced his mortgage at the lower rate after making two annual payments, how much is his remaining mortgage balance after making 3 of the lower annual payments in addition to the first two made before refinancing?
$171,886
$222,670
$195,325
$214,857
Formula sheet
A | B | C | D | E | F | G | H | I |
2 | 1) | |||||||
3 | Calculation of annual Payment: | |||||||
4 | ||||||||
5 | Annual payment can be calculated using PMT(RATE,NPER,PV,FV,TYPE) function in Excel as follows: | |||||||
6 | ||||||||
7 | Given the following data: | |||||||
8 | Loan taken | 225000 | ||||||
9 | Duration of mortgage | 25 | Years | |||||
10 | Interest rate | 0.045 | ||||||
11 | ||||||||
12 | Annual Payment can be calculated as below: | |||||||
13 | RATE (Annual interst rate): | =D10 | ||||||
14 | NPER (No of Years): | =D9 | ||||||
15 | PV (Loan Amount): | =-D8 | ||||||
16 | FV | 0 | ||||||
17 | TYPE | 0 | ||||||
18 | Annual Payment | =PMT(D13,D14,D15,D16,D17) | =PMT(D13,D14,D15,D16,D17) | |||||
19 | ||||||||
20 | Hence Annual Payment is | =D18 | ||||||
21 | Thus fourth option is correct. | |||||||
22 | ||||||||
23 | 2) | |||||||
24 | Mortgage Table will be as follows: | |||||||
25 | ||||||||
26 | Year | Beginning Balance | Annual Payment | Interest Paid | Principle Paid | Ending Balance | ||
27 | 1 | =D8 | =$D$20 | =D27*$D$10 | =E27-F27 | =D27-G27 | ||
28 | =C27+1 | =H27 | =$D$20 | =D28*$D$10 | =E28-F28 | =D28-G28 | ||
29 | =C28+1 | =H28 | =$D$20 | =D29*$D$10 | =E29-F29 | =D29-G29 | ||
30 | =C29+1 | =H29 | =$D$20 | =D30*$D$10 | =E30-F30 | =D30-G30 | ||
31 | ||||||||
32 | Hence interest paid during second year is | =F28 | ||||||
33 | Thus second option is correct. | |||||||
34 | ||||||||
35 | 3) | |||||||
36 | The refinancing payment to be made on the existing mortgage will be the present value of mortgage. | |||||||
37 | Calculation of Value of Mortgage after2nd payment: | |||||||
38 | ||||||||
39 | Value of mortage will be the present value of all the monthly payments. | |||||||
40 | ||||||||
41 | Given the following data: | |||||||
42 | Annual Payments | =D20 | ||||||
43 | Interest Rate | =D10 | ||||||
44 | Number of years remaining | =D9-2 | ||||||
45 | ||||||||
46 | ||||||||
47 | Value of loan | =Present value of annuity of monthly payments | ||||||
48 | =$15,173.78*(P/A,4.50%,23) | |||||||
49 | =D42*PV(D43,D44,-1,0) | =D42*PV(D43,D44,-1,0) | ||||||
50 | ||||||||
51 | Hence Value of loan after 96th payment is | =D49 | ||||||
52 | ||||||||
53 | Calculation of Annual Payment after refinancing: | |||||||
54 | ||||||||
55 | Monthly payment can be calculated using PMT(RATE,NPER,PV,FV,TYPE) function in Excel as follows: | |||||||
56 | ||||||||
57 | Given the following data: | |||||||
58 | Loan taken | =D51 | ||||||
59 | Duration of mortgage | =D44 | Years | |||||
60 | Interest rate | 0.035 | ||||||
61 | ||||||||
62 | Annual Payment can be calculated as below: | |||||||
63 | RATE (Annual interst rate): | =D60 | ||||||
64 | NPER (No of Years): | =D59 | ||||||
65 | PV (Loan Amount): | =-D58 | ||||||
66 | FV | 0 | ||||||
67 | TYPE | 0 | ||||||
68 | Annual Payment | =PMT(D63,D64,D65,D66,D67) | =PMT(D63,D64,D65,D66,D67) | |||||
69 | ||||||||
70 | Hence Annual Payment is | =D68 | ||||||
71 | ||||||||
72 | Calculation of profit or loss from Refinancing: | |||||||
73 | ||||||||
74 | Savings on annual Payments | =D20-D70 | =D20-D70 | |||||
75 | Present Value of Savings | =Annual Savings*(P/A,3.50%,23) | ||||||
76 | =D74*PV(D60,D59,-1,0) | =D74*PV(D60,D59,-1,0) | ||||||
77 | ||||||||
78 | Hence largest amount to be paid to secure refinancing is | =D76 | ||||||
79 | Thus first option is correct. | |||||||
80 | ||||||||
81 | 4) | |||||||
82 | ||||||||
83 | Calculation of Value of refinanced Mortgage after 3 payment: | |||||||
84 | ||||||||
85 | Value of mortage will be the present value of all the monthly payments. | |||||||
86 | ||||||||
87 | Given the following data: | |||||||
88 | Annual Payments | =D70 | ||||||
89 | Interest Rate | =D60 | ||||||
90 | Number of years remaining | =D59-3 | ||||||
91 | ||||||||
92 | ||||||||
93 | Value of loan | =Present value of annuity of monthly payments | ||||||
94 | =$13743.25*(P/A,3.50%,20) | |||||||
95 | =D88*PV(D89,D90,-1,0) | =D88*PV(D89,D90,-1,0) | ||||||
96 | ||||||||
97 | Hence Value of loan after 96th payment is | =D95 | ||||||
98 | Thus third option is correct. | |||||||
99 |
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