Question

1.         You have an initial amortizing loan (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 each annual Payment equal to?

                        A. 22,206

                        B. 23,265

                        C. 22,441

                        D. 28,120

2.         You have an initial amortizing loan (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 INTEREST you will pay at the end of year 16?

                        A. 15,724

                        B. 14,646

                        C. 14,041

                        D. 15,206

3.         You have an initial amortizing loan (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 principal you will pay at the end of year 20?

                        A. 11,108

                        B. 9,524

                        C. 10,286

                        D. 8,818

Answer 1

1.

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]

Where,

              Loan amount (P) = $250000

                Time (n) = 30

               Interest rate [r] = 8% /period

Let's put all the values in the formula to calculate EMI

EMI = 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]

        = 22206.86

Correct option is A

B.C

Period	Loan balance	Periodic Payment (EMI)	Interest	Principle Payment	Remaining Loan
0	250000
1	$ 2,50,000.00	$   22,206.86	$                 20,000.00	$      2,206.86	$      2,47,793.14
2	$ 2,47,793.14	$   22,206.86	$                 19,823.45	$      2,383.41	$      2,45,409.73
3	$ 2,45,409.73	$   22,206.86	$                 19,632.78	$      2,574.08	$      2,42,835.66
4	$ 2,42,835.66	$   22,206.86	$                 19,426.85	$      2,780.01	$      2,40,055.65
5	$ 2,40,055.65	$   22,206.86	$                 19,204.45	$      3,002.41	$      2,37,053.24
6	$ 2,37,053.24	$   22,206.86	$                 18,964.26	$      3,242.60	$      2,33,810.64
7	$ 2,33,810.64	$   22,206.86	$                 18,704.85	$      3,502.01	$      2,30,308.64
8	$ 2,30,308.64	$   22,206.86	$                 18,424.69	$     3,782.17	$      2,26,526.47
9	$ 2,26,526.47	$   22,206.86	$                 18,122.12	$      4,084.74	$      2,22,441.73
10	$ 2,22,441.73	$   22,206.86	$                 17,795.34	$      4,411.52	$      2,18,030.21
11	$ 2,18,030.21	$   22,206.86	$                 17,442.42	$      4,764.44	$      2,13,265.77
12	$ 2,13,265.77	$   22,206.86	$                 17,061.26	$      5,145.60	$      2,08,120.17
13	$ 2,08,120.17	$   22,206.86	$                 16,649.61	$      5,557.24	$      2,02,562.93
14	$ 2,02,562.93	$   22,206.86	$                 16,205.03	$      6,001.82	$      1,96,561.10
15	$ 1,96,561.10	$   22,206.86	$                 15,724.89	$      6,481.97	$      1,90,079.13
16	$ 1,90,079.13	$   22,206.86	$                 15,206.33	$      7,000.53	$      1,83,078.60
17	$ 1,83,078.60	$   22,206.86	$                 14,646.29	$      7,560.57	$      1,75,518.03
18	$ 1,75,518.03	$   22,206.86	$                 14,041.44	$      8,165.42	$      1,67,352.62
19	$ 1,67,352.62	$   22,206.86	$                 13,388.21	$      8,818.65	$      1,58,533.97
20	$ 1,58,533.97	$   22,206.86	$                 12,682.72	$      9,524.14	$      1,49,009.83

Interest Exp year 16 = 15206 (Option D)

Principle amount at year 20 = 9524 (Option B)

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