ACME Corporation constructed a small office building for their firm 5 years ago.

ID: 1221254 • Letter: A

Question

ACME Corporation constructed a small office building for their firm 5 years ago. They financed it with a bank loan for $450,000 over 15 years at 6% interest with quarterly payments and quarterly compounding. The loan can be repaid at any time without penalty.

a) How much does ACME pay per quarter on this loan?

b) ACME is preparing to make their 23rd loan payment. Hoe much will they pay in interst and principal on this payment (directly calculate these values, do not create the entire loan schedule)?

c) What is the otal amount of interest at ACME will pay on this loan?

d) Interest rates have decreases since ACME secured this financing and since there is no penalty for repaying the deby early, ACME is considering refinancing their remaining debt after maing the 23rd payment. They found that the loan can be refinanced for 4% over 20 years - stil with quarterly compounding and payments. The new loan has a 5% loan initiation fee(balance transfer fee), which will be added to the new loan. What will be ACME's new quarterly loan payment withthe refinanced loan?

e) What is the difference in total interest that ACME would pay if they refinanced compared to staying wit the original loan terms?

f) Consider these two options (the original loan terms or refinancing after the 23rd payment) and briefly discuss some factors that ACME should cnsider when deciding whether or not they should refinance the loan?

Explanation / Answer

Number of periods =15*4=60

Interest rate per quarter=6/4=1.5%

Let quarterly payment =x

Thus Loan Amount=x*Annuity factor(60 period, 1.5%)

Annuity factor (60 period, 1.5%)=(1/0.015)*(1-(1/(1+0.015))^60)= 39.38026889

Thus 450000=x*39.38026889

X=11165

Thus Quarterly payment=$11165

ACME pays $11427.04234 per quarter on this loan

Loan schedule

Quarter

Beginning amount

Interest@1.5%

Quarterly Payment

Principal paid

Ending Amount

450000.00

6750.00

11427.04

4677.04

445322.96

6679.84

11427.04

15042.20

430280.76

6454.21

11427.04

4972.83

425307.93

6379.62

11427.04

5047.42

420260.51

6303.91

11427.04

5123.13

415137.37

6227.06

11427.04

5199.98

409937.39

6149.06

11427.04

5277.98

404659.41

6069.89

11427.04

5357.15

399302.26

5989.53

11427.04

5437.51

393864.75

5907.97

11427.04

5519.07

388345.68

5825.19

11427.04

5601.86

382743.82

5741.16

11427.04

5685.89

377057.94

5655.87

11427.04

5771.17

371286.76

5569.30

11427.04

5857.74

365429.02

5481.44

11427.04

5945.61

359483.42

5392.25

11427.04

6034.79

353448.62

5301.73

11427.04

6125.31

347323.31

5209.85

11427.04

6217.19

341106.12

5116.59

11427.04

6310.45

334795.67

5021.94

11427.04

6405.11

328390.56

4925.86

11427.04

6501.18

321889.38

4828.34

11427.04

6598.70

315290.68

4729.36

11427.04

6697.68

308592.99

4628.89

11427.04

6798.15

301794.85

4526.92

11427.04

6900.12

294894.73

4423.42

11427.04

7003.62

287891.10

4318.37

11427.04

7108.68

280782.43

4211.74

11427.04

7215.31

273567.12

4103.51

11427.04

7323.54

266243.59

3993.65

11427.04

7433.39

258810.20

3882.15

11427.04

7544.89

251265.31

3768.98

11427.04

7658.06

243607.25

3654.11

11427.04

7772.93

235834.31

3537.51

11427.04

7889.53

227944.79

3419.17

11427.04

8007.87

219936.91

3299.05

11427.04

8127.99

211808.93

3177.13

11427.04

8249.91

203559.02

3053.39

11427.04

8373.66

195185.36

2927.78

11427.04

8499.26

186686.10

2800.29

11427.04

8626.75

178059.35

2670.89

11427.04

8756.15

169303.20

2539.55

11427.04

8887.49

160415.70

2406.24

11427.04

9020.81

151394.89

2270.92

11427.04

9156.12

142238.78

2133.58

11427.04

9293.46

132945.31

1994.18

11427.04

9432.86

123512.45

1852.69

11427.04

9574.36

113938.10

1709.07

11427.04

9717.97

104220.13

1563.30

11427.04

9863.74

94356.39

1415.35

11427.04

10011.70

84344.69

1265.17

11427.04

10161.87

74182.82

1112.74

11427.04

10314.30

63868.52

958.03

11427.04

10469.01

53399.50

800.99

11427.04

10626.05

42773.45

641.60

11427.04

10785.44

31988.01

479.82

11427.04

10947.22

21040.79

315.61

11427.04

11111.43

9929.36

148.94

11427.04

11278.10

-1348.74

-20.23

11427.04

11447.27

-12796.02

-191.94

11427.04

11618.98

-24415.00

Total Interest paid

221502.54

In Period 23, Interest=$4729.36

Principal paid=$6697.68

Total Amount of interest paid=$221502.54 (From the schedule)

Remaining balance after 23rd payment=308592.99 (From the schedule)

4% over 20 years means 1% per quarter with 80 periods

Thus Loan Amount=x*Annuity factor(80 period, 1%)

Annuity factor (60 period, 1.5%)=(1/0.01)*(1-(1/(1+0.01))^80)= 54.88820611

Thus 308592.99=x*54.88820611

X=5622.209431

Please repost the remaining question

Quarter

Beginning amount

Interest@1.5%

Quarterly Payment

Principal paid

Ending Amount

450000.00

6750.00

11427.04

4677.04

445322.96

6679.84

11427.04

15042.20

430280.76

6454.21

11427.04

4972.83

425307.93

6379.62

11427.04

5047.42

420260.51

6303.91

11427.04

5123.13

415137.37

6227.06

11427.04

5199.98

409937.39

6149.06

11427.04

5277.98

404659.41

6069.89

11427.04

5357.15

399302.26

5989.53

11427.04

5437.51

393864.75

5907.97

11427.04

5519.07

388345.68

5825.19

11427.04

5601.86

382743.82

5741.16

11427.04

5685.89

377057.94

5655.87

11427.04

5771.17

371286.76

5569.30

11427.04

5857.74

365429.02

5481.44

11427.04

5945.61

359483.42

5392.25

11427.04

6034.79

353448.62

5301.73

11427.04

6125.31

347323.31

5209.85

11427.04

6217.19

341106.12

5116.59

11427.04

6310.45

334795.67

5021.94

11427.04

6405.11

328390.56

4925.86

11427.04

6501.18

321889.38

4828.34

11427.04

6598.70

315290.68

4729.36

11427.04

6697.68

308592.99

4628.89

11427.04

6798.15

301794.85

4526.92

11427.04

6900.12

294894.73

4423.42

11427.04

7003.62

287891.10

4318.37

11427.04

7108.68

280782.43

4211.74

11427.04

7215.31

273567.12

4103.51

11427.04

7323.54

266243.59

3993.65

11427.04

7433.39

258810.20

3882.15

11427.04

7544.89

251265.31

3768.98

11427.04

7658.06

243607.25

3654.11

11427.04

7772.93

235834.31

3537.51

11427.04

7889.53

227944.79

3419.17

11427.04

8007.87

219936.91

3299.05

11427.04

8127.99

211808.93

3177.13

11427.04

8249.91

203559.02

3053.39

11427.04

8373.66

195185.36

2927.78

11427.04

8499.26

186686.10

2800.29

11427.04

8626.75

178059.35

2670.89

11427.04

8756.15

169303.20

2539.55

11427.04

8887.49

160415.70

2406.24

11427.04

9020.81

151394.89

2270.92

11427.04

9156.12

142238.78

2133.58

11427.04

9293.46

132945.31

1994.18

11427.04

9432.86

123512.45

1852.69

11427.04

9574.36

113938.10

1709.07

11427.04

9717.97

104220.13

1563.30

11427.04

9863.74

94356.39

1415.35

11427.04

10011.70

84344.69

1265.17

11427.04

10161.87

74182.82

1112.74

11427.04

10314.30

63868.52

958.03

11427.04

10469.01

53399.50

800.99

11427.04

10626.05

42773.45

641.60

11427.04

10785.44

31988.01

479.82

11427.04

10947.22

21040.79

315.61

11427.04

11111.43

9929.36

148.94

11427.04

11278.10

-1348.74

-20.23

11427.04

11447.27

-12796.02

-191.94

11427.04

11618.98

-24415.00

Total Interest paid

221502.54

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