Question

Present value with periodic rates. Sam​ Hinds, a local​ dentist, is going to remodel the dental reception area and add two new workstations. He has contacted​ A-Dec, and the new equipment and cabinetry will cost ​$25 comma 000. The purchase will be financed with an interest rate of 7.5​% loan over 7 years. What will Sam have to pay for this equipment if the loan calls for quarterly payments ​(4 per​ year) and monthly payments ​(12 per​ year)? Compare the annual cash outflows of the two payments. Why does the monthly payment plan have less total cash outflow each​ year?

Answer 1

Why does the monthly payment plan have less total cash outflow each​ year?

Total paym. capital Interest

Q. Totales payments 32.362,50 25.000,00 7.362,50

AnnulaTotales payments 33.040,06 25.000,00 8.040,06

Compare the annual cash outflows of the two payments.

Total paym. capital Interest

Year 1 Quarterly 4.623,21 2.826,48 1.796,74

Year 1 Annual 4.720,01 2.845,01 1.875,00

Year 2 Quarterly 4.623,21 3.044,50 1.578,71

Year 2 Annual 4.720,01 3.058,38 1.661,62

Year 3 Quarterly 4.623,21 3.279,34 1.343,87

Year 3 Annual 4.720,01 3.287,76 1.432,25

Year 4 Quarterly 4.623,21 3.532,30 1.090,92

Year 4 Annual 4.720,01 3.534,34 1.185,66

Year 5 Quarterly 4.623,21 3.804,76 818,45

Year 5 Annual 4.720,01 3.799,42 920,59

Year 6 Quarterly 4.623,21 4.098,25 524,97

Year 6 Annual 4.720,01 4.084,38 635,63

Year 7 Quarterly 4.623,21 4.414,37 208,85

Year 7 Annual 4.720,01 4.390,71 329,30

Step-by-step explanation:

Period Payment Capital Interest

1 1.155,80 687,05 468,75

2 1.155,80 699,94 455,87

3 1.155,80 713,06 442,74

4 1.155,80 726,43 429,37

5 1.155,80 740,05 415,75

6 1.155,80 753,93 401,88

7 1.155,80 768,06 387,74

8 1.155,80 782,46 373,34

9 1.155,80 797,13 358,67

10 1.155,80 812,08 343,72

11 1.155,80 827,31 328,50

12 1.155,80 842,82 312,98

13 1.155,80 858,62 297,18

14 1.155,80 874,72 281,08

15 1.155,80 891,12 264,68

16 1.155,80 907,83 247,97

17 1.155,80 924,85 230,95

18 1.155,80 942,19 213,61

19 1.155,80 959,86 195,94

20 1.155,80 977,86 177,95

21 1.155,80 996,19 159,61

22 1.155,80 1.014,87 140,93

23 1.155,80 1.033,90 121,90

24 1.155,80 1.053,29 102,52

25 1.155,80 1.073,03 82,77

26 1.155,80 1.093,15 62,65

27 1.155,80 1.113,65 42,15

28 1.155,80 1.134,53 21,27

Totales payments 32.362,50 25.000,00 7.362,50

Period Payment Capital Interest

1 4.720,01 2.845,01 1.875,00

2 4.720,01 3.058,38 1.661,62

3 4.720,01 3.287,76 1.432,25

4 4.720,01 3.534,34 1.185,66

5 4.720,01 3.799,42 920,59

6 4.720,01 4.084,38 635,63

7 4.720,01 4.390,71 329,30

Totales payments 33.040,06 25.000,00 8.040,06