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1)You invest in a fund earning simple interest of 7%
1)You invest in a fund earning simple interest of 7%. The amount that you must invest today to have 5000 at the end of 5 years is X. The amount that you must invest at the end of 5 years to have 5000 at the end of 10 years is Y.
Determine |X − Y |.
(A) 0 (B) 267 (C) 289 (D) 301 (E) 327
2)You deposit 100 into a savings account at time 0, which pays interest at a nominal rate of i, compounded semiannually. Your friend deposits 200 into a different savings account at time 0, which pays simple interest at an annual rate of i.
You and your friend earn the same amount of interest during the last 6 months of the 10th year. Calculate i.
(A) 8% (B) 7.4% (C) 6.8% (D) 6% (E) 5.2%
3)You invest 25,000 in an account earning simple interest of 5%. Your friend investsX in an account earning 2% compounded annually. In year t, you and your friend earn the same annual effective interest rate. At the end of year t, the amount of money in your account is equal to the amount of money in your friend’s account. Determine X.
(A) 25,256 (B) 30,000 (C) 34,504 (D) 36,712 (E) 38,000
Expert Solution
1)Option A is the answer.
if we discount the 5000 to the year zero then the value will be
From Year 0 to year 5.
Present Value= FutureValue/(1+rate)^t
= 5000/(1.07^5)
= 3564.93=X
discount from year 10 to year 5.
PV = 5000/(1.07^5)
= 3564.93=Y
|X-Y| = 0
Option (A) is the correct ans.
2)
Let i be the interest rate
Interest during the last 6 months of the 10th year
A10 -A9.5 = A9.5(1+i/2) - A9.5 = A9.5* i/2
A9.5 *i/2=
During last 6 months Simple interest earned =
As the interest earned is same
i = 7.4%
Ans B)7.4%
please see the attached file.
3)
First we find t. Since the amounts are equal,
25000 x (1 + 0.05t) = X x (1.02)^t
Since the annual interest rate is same, we have
0.05 x 25000/(25000 x (1+0.5(t-1)) = 0.02
62500 = 25000 + 12500(t - 1)
37500/12500 = t - 1
t = 4
Now, solving for X
30000/1.02^4 = X
X = 25256
Option A is correct.
4)
Answer 1:
Scenario 1 - Normal Condition
EBIT = $52000, Market cap = $382,500
As there is no debt, Market cap = Total equity
ROE = Net income / Equity
Now, there is no debt, hence interest = 0 and taxes are to be ignored as given in the problem
Hence, Net income = EBIT
ROE = EBIT / Market cap
= 52000 / 382500
Hence, ROE = 13.59%
Scenario 2 - Expansion in economy
EBIT will increase by 14%
So, EBIT = 1.14 * $52000 = $59280
ROE = 59280 / 382500
Hence, ROE = 15.49%
Scenario 3 - Depression in economy
EBIT will decrease by 23%
So, EBIT = 0.77 * $52000 = $40040
ROE = 40040 / 382500
Hence, ROE = 10.46%
Answer 2:
Change in ROE in expansion = (15.49 - 13.59) / 13.59 * 100 = +13.98%
Change in ROE in depression = (10.46 - 13.59) / 13.59 *100 = -23.03%
Answer 3:
Company is considering $190000 debt with 7% interest
Hence, interest = 0.07 * $190000 = $13300
Net income = EBIT - interest - taxes = $52000 - $13300 = $38700
Equity = Market cap - debt = $382,500 - $190,000 = $192,500
Scenario 1 - Normal condition
ROE = Net income / Equity
= 38700 / 192500
Hence, ROE = 20.10%
Scenario 2 - Expansion in economy
EBIT = $59280
Net income = EBIT - interest - taxes = $59280 - $13300 = $45980
ROE = 45980 / 192500
Hence, ROE = 23.88%
Scenario 3 - Depression in economy
EBIT = $40040
Net income = EBIT - interest - taxes = $40040 - $13300 = $26740
ROE = 26740 / 192500
Hence, ROE = 13.89%
Answer 4:
Change in ROE in expansion = (23.88 - 20.10) / 20.10 * 100 = +18.80%
Change in ROE in depression = (13.89 - 20.10) / 20.10 *100 = -30.89%
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