Question

In: Accounting

1.         You have an initial amortizing loan (similar to a mortgage) of $250,000, to be repaid...

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

Solutions

Expert Solution

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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