<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:
4400 Unfavorable
Explanation:
Calculation to determine the labor rate variance for the month
First step is to calculate the Standard hours using this formula
Standard hours = Standard labor-hours per unit of output*Actual output
Let plug in the formula
Standard hours= 4.5*1,300 units
Standard hours= 5850
Now let calculate the Direct labor efficiency variance using this formula
Direct labor efficiency variance = (Standard hours - Actual hours)*Standard rate
Let plug in the formula
Direct labor efficiency variance= (5,850-6,100)*17.60
Direct labor efficiency variance= 4400 Unfavorable
Therefore the labor rate variance for the month is 4400 Unfavorable
Answer:
3.63yrs
Explanation:
CExplanation: C) Investment / Annual cash flows$2,900,000 / 800,000 = 3.63 yrs
Answer:
The CPA rebuts the allegations
Explanation:
The Securities Act of 1933 requires that investors receive financial and other significant information regarding any and all securities being sold publicly and prohibits deceit, misrepresentations, and other fraud in the sale of securities. Therefore, since there was material misstatement or omission in the financial statements, the only chance the CPA has is if they rebut the allegations. Meaning that they provide actual evidence, such as physical statements or witnesses that contradict or nullify the evidence that is being presented against them regarding the material misstatement or omission
<span>I have not been an appointee of employee of any regulator at any point in the past two years. I have worked as an independent contractor for a computer company for the last 5 years. Since a regulator company is one that usually involves systematic schemes and benefits to the employee, my emoployer would not fall into the category.</span>
