In: Finance
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?
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 |