<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>
They could change for many reasons some being:
1. if you're not on a lease the rent can go up at any time only
2. if you are on a lease regardless improvements to your home the landlord can raise it every year.
3. if you have a mortgage w a variable APR your mortgage/ housing needs change monthly
4. your goals would change if maybe you wanted to move closer to your job or you got a new job and you need to move closer
5. maybe if you got married or had kids your housing gold would change.
6. maybe you live in not such a nice neighborhood and you'd like to live in a neighborhood less crime your goals would change
not sure if those are the answers you're looking for but there's so many different reasons that your housing needs and goals could change
Answer:
c. May be able to avoid liability to the extent she had no reason to know of the deficiency (and did not have actual knowledge) when filing the return. The burden of proof will be on her.
Explanation:
The doctrine of <em>innocent spouse relief</em> might apply here. Mrs. Jones will have to prove that:
- the income that was omitted was earned by her husband, not her.
- she must prove that when she signed the tax filings, she was not aware of the omission.
- after examining all the facts surrounding the omission, the IRS must decide that blaming her would not be fair.
Answer:
E. $2,688.77
Explanation:
We need to calculate the PMT of an ordinary annuity at 6%
PV 402,000
time:
85 years - 62 years = 23 years of retirement
23 years x 12 months per year = 276 months
rate: 6% annual rate we must divide over 12 months to convert into monthly: 0.06/12 = 0.005
C $ 2,688.766
<em>She can withdraw 2,688.76 per month</em>
The statements are:
Because Dazzle is not a separate tax entity, all the owners declare revenue earned through the company on their personal federal tax returns.
The $5 million dollar villa is protected from business liabilities unless the liability is incurred through wrongful acts.
