You bought a duplex exactly 9 years ago. You paid $56,000 for the duplex. The la
ID: 2553737 • Letter: Y
Question
You bought a duplex exactly 9 years ago. You paid $56,000 for the duplex. The land was worth $6,000 when you bought the duplex. You made a 20% down payment and financed the balance for 30 years at 10.5%. The loan was fully amortized with monthly payments and you paid 3 points so the lender would fix the rate for the term of the loan. You have a need for money now and wish to borrow against the property via a second mortgage. The property has appreciated 8% per year. The second mortgage terms are 14.5%, 15 years monthly payments, fully amortizing, 80% loan to value ratio, with no points required. You depreciated the improvements for 15 years using a straight line technique. Show work below please. a. Effective interest rate on 1st mortgage b. What is the book value of the property today at the end of the gth year? c. How many dollars did you borrow using the second mortgage? d. How many you owe on the property in 5 years?Explanation / Answer
Answer a: Details
Sr. No.
Particulars
Amount $
1.
Cost of the property when bought
56,000
2.
Less: Down Payment @ 20% [56,000*20%]
11,200
3.
Loan Value [1-2]
44,800
4.
Interest Rate (compounded monthly assumed) (i)
10.5%
5.
Years (n)
30
Calculation of Effective Interest Rate
Sr. No.
Particulars
Details
Amount $
1.
Calculation of Effective interest
Formula
(1+i/n)^n-1
Amount
=[(1+0.105/30)^30-1]*100 %
=[(1.0035)^30-1]*100 %
=0.110507*100 %
=11.05 %
Note: It is assumed that loan is compounded monthly in absence of information
Answer b.
Sr. No.
Particulars
Amount $
1.
Cost of the property when bought
56,000
2.
Less: Land Value
6,000
3.
Cost of Building
50,000
4.
Depreciation under Straight Line method
(=50000/15)
3,333
5.
Depreciation for 15 years
30,000
6.
Appreciation @ 8% per year *
55,944
7.
Book Value of Property
[$ 56,000-30,000+55,944]
81,944
* Calculation of Appreciation
Sr. No.
Particulars
UOM
1.
Principal (p)
$ Amt
56,000
2.
Rate of increase(r)
%
8
3.
No of years (n)
Years
9
4.
Calculation of Interest
Formula
P[(1+r)^n-1]
5.
Appreciation
$ Amt
=56,000[(1+0.08)^9-1]
=56,000*0.999005
=55,944
Note: Depreciation is not charged on Land Value only on the value of Building
Answer c. Second Mortgage Details
Sr. No.
Particulars
1.
Rate of Interest
14.5%
2.
Term
15 years
3.
Loan to Value Ratio
80%
4.
Value of Property
81,944
5.
Loan @ 80% of Above
65,555
Answer d:
Details
Sr. No.
Particulars
Details
First Mortgage
Second Mortgage
1.
Loan Value (P)
$
44,800
65,555
2.
Rate of Interest (R)
%
10.5
14.5
3.
Period of interest
years
30
15
4.
No of Months
Months
360
180
5.
EMI
Formula
=[P x R x (1+R)^N]/[(1+R)^N-1]
(R)
=10.5/(12*100)
=0.00875
=14.5/(12*100)
=0.01208
Calculation
=[44800*0.00875*(1+0.00875)^360]/
[1+0.00875^360-1]
=9023.255/22.01851
=409.803
=[65555*0.01208*(1+0.01208)^180]/
[1+0.01208^180-1]
=6876.136/7.683
=894.9762
6.
Total Due
$
147,529.08
161,095.72
7.
EMI paid months
Months
=14*12
=168
=5*12
=60
8.
EMI Amount
$
68,846.904
53698.572
9.
EMI Due
$
78,682.176
107397.148
Sr. No.
Particulars
Amount $
1.
Cost of the property when bought
56,000
2.
Less: Down Payment @ 20% [56,000*20%]
11,200
3.
Loan Value [1-2]
44,800
4.
Interest Rate (compounded monthly assumed) (i)
10.5%
5.
Years (n)
30
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