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21. Dr. Rock takes out a loan for 100.000. The annual effective interest rate on the loan is 10%. Dr. Rock repays the loan by

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Answer #1

(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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