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1.Sarah Wiggum would like to make a single investment and have $1.9 million at the time of her retirement in 28 years. She has found a mutual fund that will earn 5 percent annually. How much will Sarah have to invest today? If Sarah earned an annual return of 15 percent, how soon could she then retire? a. If Sarah can earn 5 percent annually for the next 28 years, the amount of money she will have to invest today is $ (Round to the nearest cent.)
2.A 1 year call option with a strike price of $7 is selling for $1.75. The stock price is currently $6.
a. What is the price of the corresponding put having the same expiry and exercise price? The present value of the exercise price is $4.
b. The put is currently selling at $0.30. Is the put over- or under-priced?
c. What steps would you take to make an arbitrage profit? (Don't need calculations for part C - just explain please!)
3. How many years will it take for $520 to grow to $1,036.54 if it's invested at 8 percent compounded annually? The number of years it will take for $520 to grow to $1,036.54 at 8 percent compounded annually is years (Round to one decimal place)
1.Present value= future value/ (1+r)n
N=28
R=5
Future value $ 1.9 M
Present value = $ 1.900,000/ (1.05)28
=$ 1.900,000/3.920
=$484,694
Finding n if r=15
Future value= present (1+r)n
1,900,000=484,694(1.15)n
1.15n=1,900.000/484,694
1.15n=3.920
From future table
,N= 9.77 years
2.
As per call put parity
Price of call option + Present value of strike price = Price of put option + Spot price
Thus 1.75 + 4 = Price of put option + 6
5.75 = Price of put option + 6
Thus Price of put option = -0.25
Price of put option can't be negative hence price of put option = 0
b) If put option is trading at $ 0.3 , than it is over valued as theoritically value of put option should be 0
c) To Arbitrage , one can sell put option and can buy equivalent of underlying shares. This will create zero risk based strategy and will generate profit
3.
| Years | Begining balance | Interest 8% | Ending balance |
| 1 | 520.00 | 41.60 | 561.60 |
| 2 | 561.60 | 44.93 | 606.53 |
| 3 | 606.53 | 48.52 | 655.05 |
| 4 | 655.05 | 52.40 | 707.45 |
| 5 | 707.45 | 56.60 | 764.05 |
| 6 | 764.05 | 61.12 | 825.17 |
| 7 | 825.17 | 66.01 | 891.18 |
| 8 | 891.18 | 71.29 | 962.47 |
| 9 | 962.47 | 77.00 | 1039.47 |
We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
1036.54=520*(1.08)n
(1036.54/520)=(1.08)n
Taking log on both sides;
log (1036.54/520)=n*log 1.08
n=log (1036.54/520)/log 1.08
=8.99 years or 9 years
