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You’ve purchased your first home. The property taxes on it are $3 500 per year.

ID: 2580237 • Letter: Y

Question

You’ve purchased your first home. The property taxes on it are $3 500 per year. The mortgage stipulates that the owner must pay 1/12 of the annual taxes each month to the bank so that the taxes can be paid on April 1. Your first payment is at the end of April and the last payment is at the end of March of the following year. Assume that cost of money is 6.5% nominal annual interest, compounded monthly.

a. Draw the cash flow diagram for one year.

b. What is the effective annual interest rate (in %)?

c. Determine how much profit (in $) the mortgage company makes each year on the owner's tax money. Profit in this case is the difference in the sum of the amount you pay and the amount paid in property taxes.

Explanation / Answer

Effective Interest rate compounded monthly

                = P (1+ ­­    int    )12

                              12*100

                = 1 (1 +   6.5   )12

                                1200

                = 1.06697

                = 6.70%

Computation of actual profit made my mortgage company:

Compunding

Month

Installment

factor @ 6.5%

Compounded

(3500/12)

compounded

Amount

monthly

1

291.6667

1.0670

311.20

2

291.6667

1.0612

309.52

3

291.6667

1.0555

307.86

4

291.6667

1.0498

306.20

5

291.6667

1.0442

304.55

6

291.6667

1.0385

302.90

7

291.6667

1.0329

301.26

8

291.6667

1.0274

299.65

9

291.6667

1.0218

298.04

10

291.6667

1.0163

296.43

11

291.6667

1.0109

294.83

12

291.6667

1.0054

293.25

Total

3625.69

-Installment

3500.00

Net Profit

125.69

Effective Interest Earned

3.59%

Compunding

Month

Installment

factor @ 6.5%

Compounded

(3500/12)

compounded

Amount

monthly

1

291.6667

1.0670

311.20

2

291.6667

1.0612

309.52

3

291.6667

1.0555

307.86

4

291.6667

1.0498

306.20

5

291.6667

1.0442

304.55

6

291.6667

1.0385

302.90

7

291.6667

1.0329

301.26

8

291.6667

1.0274

299.65

9

291.6667

1.0218

298.04

10

291.6667

1.0163

296.43

11

291.6667

1.0109

294.83

12

291.6667

1.0054

293.25

Total

3625.69

-Installment

3500.00

Net Profit

125.69

Effective Interest Earned

3.59%