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Stock Market
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Problem 1
Compute the face value of a 30-year, fixed-rate mortgage with a monthly payment of $1, 100, assuming a nominal interest rate of 9% and a real interest rate of 11%. If the mortgage requires 5% down, what is maximum house price?
Solution:
LV = Pann*(PVIFAI, N) LV = (1, 100*12)* (PVIFA 9%, 30)= 135, 616.8
Is maximum house price
Problem 2
You need to finance the purchase of an apartment and want to obtain the 15-year loan from the TuranAlem Bank. The apartment costs 130 000 $. You are required to pay the down payment of 25%. The interest rate on a mortgage is 10%. The mortgage is monthly amortised. According to the bank policy the monthly payment should not exceed the 50% out of your current salary. Will you be able to receive the mortgage if you net current salary is 2500$ per month?
You can use the table below or a financial calculator to solve the problem.
| Present Value Interest Factor at Various Rates of Interest | ||||||
| Payment period | 5% | 6% | 7% | 8% | 9% | 10% |
| 10, 3797 | 9, 7122 | 9, 1079 | 8, 5595 | 8, 0607 | 7, 6061 | |
| 12, 4622 | 11, 4699 | 10, 594 | 9, 8181 | 9, 1285 | 8, 5136 | |
| 14, 0939 | 12, 7834 | 11, 6536 | 10, 6748 | 9, 8226 | 9, 077 | |
| 15, 3725 | 13, 7614 | 12, 409 | 11, 2578 |
Solution:
PV = PMT(1+i/m) -1 + PMT(1+i/m) -2+ … PMT(1+i/m) -n =
PMT[(1+i/m) -1 + (1+i/m) -2+ … PMT(1+i/m) -n]
PMT = PV / {1 - 1/(1+i/m) mn}
I/m
- Amount loaned: 97500$.
- 97500$ = Pann (PVIFA 10%, 15)
Pann = 97500$ / 7.6061 = 12818.659 per year
P month = 12818.659 /12 = 1068.22
3. PMT (fin Calc) = 1047.74 $
Problem 3
Compute the required monthly payment on $80, 000 30-year, fixed-rate mortgage with a nominal interest rate of 6%. Answer the following questions:
a) How many payment periods do you have? N = 360
b) What is the monthly interest rate? I = 0.06/12
c) What is the present value of the mortgage? PV = 80, 000
d) What is the future value of the mortgage? FV = 0
e) What will be the monthly mortgage payment applying the PVIFA table?
f) How much of the payment goes toward principal and interest during the first 3 month if the monthly payment is? You have to build the amortization table.
| Month | Beginning Balance | Payment | Interest Paid | Principal Paid | Ending Balance |
Solution: From Table: PMT = 484.32
The amortization schedule is as follows, PMT = 484.32:
| Month | Beginning Balance | Payment | Interest Paid | Principal Paid | Ending Balance |
| $80, 000 | $484.32 | $400 | $84.32 | $79, 915.68 | |
| $79, 915.68 | $484.32 | $399.58 | $84.74 | $79, 830.94 | |
| $79, 830.94 | $484.32 | $399.15 | $85.17 | $79, 745.77 | |
Stock Market
Consider the following security information for 4 securities making up an index:
| Security | Price | Shares Outstanding | |
| time 0 | time 1 | ||
| 20 million | |||
| 50 million | |||
| 120 million | |||
| 75 million |
What is the change in the value of the index from time 0 to time 1 if the index is calculated using a value-weighted arithmetic mean?
Solution: For a value-weighted arithmetic mean, the change is calculated as follows:
First, the market value at time 0 is calculated as:
| Security | Price | Shares Outstanding | Market Value | |
| time 0 | time 1 | |||
| 20 million | $160 | |||
| 50 million | $1, 100 | |||
| 120 million | $4, 200 | |||
| 75 million | $3, 750 | |||
| $9, 210 |
The change is then calculated as:
Index1 = Index0 ´ 1.0027