(a): Dr. Rock makes a total of 23 payments over a period of 23 years.
(b): The final payment amount = $811.66. Of this $73.79 is the interest amount and $737.87 is the principal amount. After this payment the loan outstanding becomes nil.
Calculations and explanations: For this purpose I have made a loan amortization table. In the 1st year balance at the start = $100,000 and interest amount = 10% of 100,000 = $10,000. Thus payment amount = 10000*3 = $30,000. Of this principal repayment = 30,000 – interest = 30,000 – 10,000 = $20,000. Thus balance due at the end of year 1 = 100,000 – 20,000 = 80,000. We keep on doing this for subsequent years until we arrive at the 23rd year. Here balance due at start = 737.87 and so interest = 10% of 737.87 = 73.79. So total payment = 737.87 + 73.79 = 811.66. This is less than 1,000.
The table is shown below:
Year | Balance due at the start of the year | Interest amount @ 10% | Total payment | Principal payment | Balance due at the end of the year |
1 | 100,000.00 | 10,000.00 | 30,000.00 | 20,000.00 | 80,000.00 |
2 | 80,000.00 | 8,000.00 | 24,000.00 | 16,000.00 | 64,000.00 |
3 | 64,000.00 | 6,400.00 | 19,200.00 | 12,800.00 | 51,200.00 |
4 | 51,200.00 | 5,120.00 | 15,360.00 | 10,240.00 | 40,960.00 |
5 | 40,960.00 | 4,096.00 | 12,288.00 | 8,192.00 | 32,768.00 |
6 | 32,768.00 | 3,276.80 | 9,830.40 | 6,553.60 | 26,214.40 |
7 | 26,214.40 | 2,621.44 | 7,864.32 | 5,242.88 | 20,971.52 |
8 | 20,971.52 | 2,097.15 | 6,291.46 | 4,194.30 | 16,777.22 |
9 | 16,777.22 | 1,677.72 | 5,033.16 | 3,355.44 | 13,421.77 |
10 | 13,421.77 | 1,342.18 | 4,026.53 | 2,684.35 | 10,737.42 |
11 | 10,737.42 | 1,073.74 | 3,221.23 | 2,147.48 | 8,589.93 |
12 | 8,589.93 | 858.99 | 2,576.98 | 1,717.99 | 6,871.95 |
13 | 6,871.95 | 687.19 | 2,061.58 | 1,374.39 | 5,497.56 |
14 | 5,497.56 | 549.76 | 1,649.27 | 1,099.51 | 4,398.05 |
15 | 4,398.05 | 439.80 | 1,319.41 | 879.61 | 3,518.44 |
16 | 3,518.44 | 351.84 | 1,055.53 | 703.69 | 2,814.75 |
17 | 2,814.75 | 281.47 | 844.42 | 562.95 | 2,251.80 |
18 | 2,251.80 | 225.18 | 675.54 | 450.36 | 1,801.44 |
19 | 1,801.44 | 180.14 | 540.43 | 360.29 | 1,441.15 |
20 | 1,441.15 | 144.12 | 432.35 | 288.23 | 1,152.92 |
21 | 1,152.92 | 115.29 | 345.88 | 230.58 | 922.34 |
22 | 922.34 | 92.23 | 276.70 | 184.47 | 737.87 |
23 | 737.87 | 73.79 | 811.66 | 737.87 | - |
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