Question
In: Finance
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 10 months agoRelated Solutions
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