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%
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