Answer:
It will take 51 months.
Explanation:
As we know the constant payment of $290 monthly is the annuity payment to pay $12,000 with interest rate of 0.84% per month. The Number of Months can be calculated by following formula.
Loan amount = PV = $12,000
Rate of interest = r = 0.84 %
Monthly Payment = P = $290
PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]
$12,000 = $290 x [ ( 1 - ( 1 + 0.84% )^-n / 0.84% ]
$12000 x 0.84% / $290 = 1 - ( 1 + 0.84% )^-n
0.347586 = 1 - ( 1 + 0.84% )^-n
0.347586 - 1 = - ( 1 + 0.84% )^-n
-0.652414 = - ( 1 + 0.84% )^-n
1 / 0.652414 = 1.0084^n
1.532769 = 1.0084^n
Log 1.532769 = n x log 1.0084
n = Log 1.532769 / log 1.0084
n = 51
Answer:
$14038
Explanation:
The company has marginal revenue R'(t) = 
. Therefore its revenue R(t) is given as;
R(t) = ∫R'(t)
R(t)= ∫ dt = + c
R(t) = + c
But R(0) = 0, therefore:
R(0) = 
+ c = 0
+ c = 0
100 + c =0
c = -100
Also the marginal cost per day is given by C'(t) = 140 - 0.3t
C'(t) = 140 - 0.3t
C(t) = ∫C(t) = ∫ (140 - 0.3t) dt = 140t - (0.3/2) t² + C
But C(0) = 0
C(0) = 140 (0) - (0.3/2)(0)² + c = 0
c = 0
C(0) = 140t - (0.3/2) t²
Profit P(t) = R(T) - C(T) , hence the total profit from t = 0 to t = 5 is given as:
P(t) = ![\int\limits^0_5 {[R'(t)-C'(t)]} \, dt =\int\limits^0_5 {([100e^t-(140-0.3t)]} \, dt=\int\limits^0_5 {100e^t} \, dt +\int\limits^0_5 {-0.3t} \, dt +\int\limits^0_5 {-140} \, dt \\\\=[100e^t]_0^5+[ -140t]_0^5+[-0.3t^2/2]_0^5=[14841.316-100]+[-700]+[-3.75]=14038](https://tex.z-dn.net/?f=%5Cint%5Climits%5E0_5%20%7B%5BR%27%28t%29-C%27%28t%29%5D%7D%20%5C%2C%20dt%20%3D%5Cint%5Climits%5E0_5%20%7B%28%5B100e%5Et-%28140-0.3t%29%5D%7D%20%5C%2C%20dt%3D%5Cint%5Climits%5E0_5%20%7B100e%5Et%7D%20%5C%2C%20dt%20%20%2B%5Cint%5Climits%5E0_5%20%7B-0.3t%7D%20%5C%2C%20dt%20%20%2B%5Cint%5Climits%5E0_5%20%7B-140%7D%20%5C%2C%20dt%20%20%5C%5C%5C%5C%3D%5B100e%5Et%5D_0%5E5%2B%5B%20-140t%5D_0%5E5%2B%5B-0.3t%5E2%2F2%5D_0%5E5%3D%5B14841.316-100%5D%2B%5B-700%5D%2B%5B-3.75%5D%3D14038)
The profit is $14038
Answer:
$160,000
Explanation:
If the beverage sales represent 20% of the total sales, to find out the dollar amount of beverage sales, all we need to do is multiply the total sales x 20%:
beverage sales = $800,000 x 20% = $160,000
food sales = total sales - beverage sales = $800,000 - $160,000 = $640,000
There is some information in the table that is not needed in this problem. To find real per capita GDP in 1933 measured in 2008 prices, just multiply Nominal per capita GDP in 1933 by how many times expensive the prices are in 2008 than they were in 1933. The solution is $444 x 14 = $6,216. So, the answer is $6,216.
Answer:
The actual cash value a person would receive for a $4,500 destroyed furniture would be:
$3,000
Explanation:
Actual cash value is a method to calculate the value of an insured good. Its formula goes like this: Original value minus the original value divided by the years covered multiplied by two. In our case this would be 4,500-[4,500 / 6 x 2] giving us as result the following operation 4,500- 1500 = 3,000.
