<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:
They offer shares and release their company on the stock market to be publicly traded.
Explanation:
Resembled to more developed countries, slight developed countries have a higher ratio of workers in the condition of goods and services the tertiary sector most individuals must produce food for their survival sector of the economizing.
<h3>What is the difference between a more developed country and a less developed country?</h3>
A developed country is a government that has a high level of automation and per capita income while a developing country is a country that is still in the early phases of industrial development and has a low per capita revenue.
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Answer:
The account that includes transactions like imports and exports, income earned by Americans abroad, and net transfers to other countries.
Explanation:
A current account can be defined as an account that record the different transactions a country carries out with another country. A current account comprises of net primary income, earnings from foreign investors that have occurred within a particular period of time.
Almost all countries are involved in trading of goods and services with another country, a current account helps to evaluate the manner in which a particular country traded their different goods with foreign markets.There tends to be a postive balance of a country exports more goods than it imports.
When retained earnings are not enough to meet their long-term funding needs, businesses may be able to raise funds by <u>selling common stock</u>. Long-term funding can be defined as any financial tool with maturity going beyond one year (such as bank loans, bonds, leasing and other forms of debt finance), and public and private equity instruments.
<h3>What is a retained earnings?</h3>
Retained earnings are the total of profit an establishment has left over after paying all its direct costs, indirect costs, income taxes and its dividends to shareholders.
Therefore, the correct answer is as given above
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