Question

3.You have an initial amortizing load (similar to a mortgage) of $250,000, to be repaid in equal 30 payments, over 30 years. The annual interest rate is 8%. What is the amount of principle you will pay at the end of year 20?

A.11,108

B.9,524

C.10,286

D.8,818

Answer 1

First we need to find annual payment.

If the loan amount is P, rate on interest (monthly is r, and loan term is n the EMI will be

EMI= P*r[(1 +r)^n]/ [(1+ r)^n- 1]

= 250000*0.08[(1 +0.08)^30]/ [(1+ 0.08)^30- 1]

= 20000[(1.08)^30]/ [(1.08)^30- 1]

= 20000[10.0626568891]/ [10.0626568891- 1]

= 20000[10.0626568891]/ [9.0626568891]

= 20000[1.11034291734058]

= 22206.858

Let’s prepare loan amortization schedule now

Payment	Loan balance	Annual payment	Interest	Principle	Loan balance remaining
1	250000	22206.86	20000	2206.86	247793.14
2	247793.14	22206.86	19823.4512	2383.4088	245409.7312
3	245409.7312	22206.86	19632.7785	2574.081504	242835.6497
4	242835.6497	22206.86	19426.85198	2780.008024	240055.6417
5	240055.6417	22206.86	19204.45133	3002.408666	237053.233
6	237053.233	22206.86	18964.25864	3242.60136	233810.6316
7	233810.6316	22206.86	18704.85053	3502.009468	230308.6222
8	230308.6222	22206.86	18424.68977	3782.170226	226526.452
9	226526.452	22206.86	18122.11616	4084.743844	222441.7081
10	222441.7081	22206.86	17795.33665	4411.523351	218030.1848
11	218030.1848	22206.86	17442.41478	4764.445219	213265.7395
12	213265.7395	22206.86	17061.25916	5145.600837	208120.1387
13	208120.1387	22206.86	16649.6111	5557.248904	202562.8898
14	202562.8898	22206.86	16205.03118	6001.828816	196561.061
15	196561.061	22206.86	15724.88488	6481.975122	190079.0859
16	190079.0859	22206.86	15206.32687	7000.533131	183078.5527
17	183078.5527	22206.86	14646.28422	7560.575782	175517.9769
18	175517.9769	22206.86	14041.43816	8165.421844	167352.5551
19	167352.5551	22206.86	13388.20441	8818.655592	158533.8995
20	158533.8995	22206.86	12682.71196	9524.148039	149009.7515

Principle mount paid in year 20 is 9524.