<span>Annual = Years = 6.64; Actually 7 years
Monthly = Years = 6.33; 6 Years, 4 months
Daily = Years = 6.30; 6 Years, 111 days
Continuously = 6.30; 6 Years, 110 days
The formula for compound interest is
FV = P*(1 + R/n)^(nt)
where
FV = Future Value
P = Principle
R = Annual interest rate
n = number of periods per year
t = number of years
For this problem, we can ignore p and concentrate on the (1+R/n)^(nt) term, looking for where it becomes 2. So let's use this simplified formula:
2 = (1 + R/n)^(nt)
With R, n, and t having the same meaning as in the original formula.
For for the case of compounding annually
2 = (1 + R/n)^(nt)
2 = (1 + 0.11/1)^(1t)
2 = (1.11)^t
The above equation is effectively asking for the logarithm of 2 using a base of 1.11. To do this take the log of 2 and divide by the log of 1.11. So
log(2) / log(1.11) = 0.301029996 / 0.045322979 = 6.641884618
This explanation of creating logarithms to arbitrary bases will not be repeated for the other problems.
The value of 6.641884618 indicates that many periods is needed. 6 is too low giving an increase of
1.11^6 =1.870414552
and 7 is too high, giving an increase of 1.11^7 = 2.076160153
But for the purpose of this problem, I'll say you double your money after 7 years.
For compounding monthly:
2 = (1 + R/n)^(nt)
2 = (1 + 0.11/12)^(12t)
2 = (1 + 0.009166667)^(12t)
2 = 1.009166667^(12t)
log(2)/log(1.009166667) = 0.301029996 / 0.003962897 = 75.96210258
And since the logarithm is actually 12*t, divide by 12
75.96210258 / 12 = 6.330175215
Which is 6 years and 4 months.
For compounding daily:
2 = (1 + 0.11/365)^(365t)
2 = (1 + 0.00030137)^(365t)
2 = 1.00030137^(365t)
log(2)/log(1.00030137) = 0.301029996 / 0.000130864 = 2300.334928
2300.334928 / 365 = 6.302287474
Continuously:
For continuous compounding, there's a bit of calculus required and the final formula is
FV = Pe^(rt)
where
FV = Future value
P = Principle
e = mathematical constant e. Approximately 2.718281828
r = Interest rate
t = time in years
Just as before, we'll simplify the formula and use
2 = e^(rt)
Since we have the function ln(x) which is the natural log of x, I won't bother doing log conversions.
rt = ln(2)
0.11 * t = 0.693147181
t = 0.693147181 / 0.11
t = 6.301338005</span>
Answer:
$11.98
Explanation:
A share of common stock just made a dividend payment of $1.00
The expected long-run growth rate of for this stock is 5.4%
= 5.4/100
= 0.054
The investors required rate of return is 14.2%
= 14.2/100
= 0.142
The first step is to calculate the dividend year 1(D1)
D1= Do(1+g)
= 1(1+0.054)
= 1×1.054
= $1.054
Therefore, the stock price can be calculated as follows
Po= D1/(rs-g)
= 1.054/(0.142-0.054)
= 1.054/0.088
= $11.98
Hence the Stock price is $11.98
Answer:
$59,900
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Explanation:
<u>Cash flow from Financing activities</u>
Particulars Amount
Cash paid for treasury stock $20,400
Cash dividends <u>$39,500</u>
Net cash used by financing activities <u>$59,900</u>
Answer:
Option C is the correct option.
Explanation:
As the rights and obligation of the antique rocking chair are been passed to third party, so the damage caused by the checque been bounced is the monetry consideration agreed between the party to the contract, McGraw and Tellis. So Tellis may recover money damages from McGraw. However there is a special condition that can allow Tellis recover his asset from Rio if the third party knew before purchase of this asset, that the checque paid to Tellis by McGraw was dishonoured but still he contracted with McGraw to acquire the antique rocking chair.
Overall the option C is the correct option with which the case scenario relates.
Answer: The answer is B mail carriers
Explanation:
