<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>
If a manufacturing unit uses all its resources efficiently, the production rate of the unit will increase. The waste produced will be minimized and more profit will be gained. The manufacturing unit will also have a greater opportunity of being improved.<span />
Answer:
An adjustment to retained earnings is necessary when when there is a change from LIFO to FIFO.
Calculating the effect on retained earnings:
- In the year 1 company followed LIFO and recorded ending inventory at $177500. Had it followed FIFO it would have recorded at $195000. So there would be increase in income of $17500 (195000 - 177500).
- In year 2 it followed LIFO and recorded opening inventory at $177500 and closing inventory at $355000 and thereby recording Net closing stock of $177500 (355000 - 177500). Had it followed FIFO it would have recorded a net stock of $195000.(390000-195000). So there would be increase in income by of $17500 (195000 - 177500).
So in total of 2 years there would be an increase of $35000 Net income i.e., Retained earnings and increase in stock value of $35000.
The journal entry is:
Inventory A/c Dr $35,000
To Retained earnings A/c $35,000
Explanation:
<span>Electra experienced in this case the effect of legal, regulatory differences between the different markets in which they wished to introduce their new product. By choosing to use the lower motor speed, they eliminated the need to redesign the product for the various markets. Instead, one product could be produced and distributed worldwide.</span>
<span>The demand for gold toe socks is likely to be more elastic than the demand for power tools because, generally speaking, power tools would be a bit more expensive than gold toe socks would be, and they also may have more substitutes than power tools would have.</span>
