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Richard borrowed 50,000 from a bank at 12% (APR) semiannually compounded interest to be repaid in...

Richard borrowed 50,000 from a bank at 12% (APR) semiannually compounded interest to be repaid in 10 years (12 equal installments) . Calculate the interest and principal paid in the fourth year. USE EXCEL FORMULAS SO I CAN SEE THE INPUTS PLEASE AND SHOW THE WORK I WANT TO LEARN IT!

Solutions

Expert Solution

We are given the following information:

Loan Period 10
Interest rate 12%
PMT frequency 2
Loan amount 50000

We need to solve the following equation to arrive at the required PMT

So the PMT is $4359.23. We can get the following schedule:

Year Opening Balance Loan PMT Interest Principal repayment Closing Balance
0 50000 50000
1 50000 4359.22785 3000 1359.227849 48640.77215
2 48640.77215 4359.22785 2918.446329 1440.78152 47199.99063
3 47199.99063 4359.22785 2831.999438 1527.228411 45672.76222
4 45672.76222 4359.22785 2740.365733 1618.862116 44053.9001
5 44053.9001 4359.22785 2643.234006 1715.993843 42337.90626
6 42337.90626 4359.22785 2540.274376 1818.953473 40518.95279
7 40518.95279 4359.22785 2431.137167 1928.090681 38590.86211
8 38590.86211 4359.22785 2315.451726 2043.776122 36547.08599
9 36547.08599 4359.22785 2192.825159 2166.40269 34380.6833
10 34380.6833 4359.22785 2062.840998 2296.386851 32084.29644
11 32084.29644 4359.22785 1925.057787 2434.170062 29650.12638
12 29650.12638 4359.22785 1779.007583 2580.220266 27069.90612
13 27069.90612 4359.22785 1624.194367 2735.033482 24334.87263
14 24334.87263 4359.22785 1460.092358 2899.135491 21435.73714
15 21435.73714 4359.22785 1286.144229 3073.08362 18362.65352
16 18362.65352 4359.22785 1101.759211 3257.468637 15105.18489
17 15105.18489 4359.22785 906.3110932 3452.916756 11652.26813
18 11652.26813 4359.22785 699.1360878 3660.091761 7992.176369
19 7992.176369 4359.22785 479.5305822 3879.697267 4112.479103
20 4112.479103 4359.22785 246.7487462 4112.479103 0
87184.557 37184.55698 50000
  • Opening balance = previous year's closing balance
  • Closing balance = Opening balance+Loan-Principal repayment
  • PMT is calculated as per the above formula
  • Interest = 0.12 x opening balance
  • Principal repayment = PMT - Interest
  • The yellow marked rows are for year 4. As there are semiannual payments, so first 6 rows are fore years 1-3
  • Interest paid in year 4 = 4746.588894  
  • Principal repaid in year 4 = 3971.866804

jeff jeffy answered 9 months ago
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