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!

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
$PV=PMT \times \frac{1-(1+\frac{r}{frequency})^{-n\times frequency}}{\frac{r}{frequency}}$

$50000=PMT \times \frac{1-(1+\frac{0.12}{2})^{-10\times2}}{\frac{0.12}{2}}$

$PMT=4359.23$

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 3 months ago

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

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