Question

In: Finance

In purchasing a house that is worth $175,000, you need to obtain a mortgage. Suppose you...

In purchasing a house that is worth $175,000, you need to obtain a mortgage. Suppose you choose a 30year fixed rate mortgage with an interest rate/year of 9.74%. What is the annual payment required? How much of each year's payment goes to paying interest and how much to reducing the principal balance for the first 15 years?

Solutions

Expert Solution

Annual rate(M)= yearly rate/1= 9.74% Annual payment= 18162.44
Year Beginning balance (A) Annual payment Interest = M*A Principal paid Ending balance
1 175000.00 18162.44 17045.00 1117.44 173882.56
2 173882.56 18162.44 16936.16 1226.28 172656.27
3 172656.27 18162.44 16816.72 1345.72 171310.55
4 171310.55 18162.44 16685.65 1476.80 169833.76
5 169833.76 18162.44 16541.81 1620.64 168213.12
6 168213.12 18162.44 16383.96 1778.49 166434.63
7 166434.63 18162.44 16210.73 1951.71 164482.92
8 164482.92 18162.44 16020.64 2141.81 162341.12
9 162341.12 18162.44 15812.02 2350.42 159990.70
10 159990.70 18162.44 15583.09 2579.35 157411.35
11 157411.35 18162.44 15331.87 2830.58 154580.77
12 154580.77 18162.44 15056.17 3106.28 151474.49
13 151474.49 18162.44 14753.62 3408.83 148065.67
14 148065.67 18162.44 14421.60 3740.85 144324.82
15 144324.82 18162.44 14057.24 4105.21 140219.61
16 140219.61 18162.44 13657.39 4505.05 135714.56
17 135714.56 18162.44 13218.60 4943.85 130770.71
18 130770.71 18162.44 12737.07 5425.38 125345.34
19 125345.34 18162.44 12208.64 5953.81 119391.53
20 119391.53 18162.44 11628.73 6533.71 112857.82
21 112857.82 18162.44 10992.35 7170.09 105687.73
22 105687.73 18162.44 10293.98 7868.46 97819.27
23 97819.27 18162.44 9527.60 8634.85 89184.42
24 89184.42 18162.44 8686.56 9475.88 79708.54
25 79708.54 18162.44 7763.61 10398.83 69309.71
26 69309.71 18162.44 6750.77 11411.68 57898.03
27 57898.03 18162.44 5639.27 12523.18 45374.86
28 45374.86 18162.44 4419.51 13742.93 31631.93
29 31631.93 18162.44 3080.95 15081.49 16550.43
30 16550.43 18162.44 1612.01 16550.43 0.00
Where
Interest paid = Beginning balance * Annual interest rate
Principal = Annual payment – interest paid
Ending balance = beginning balance – principal paid
Beginning balance = previous Year ending balance

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