Answer:
a. 4 years
b. 19 years
c. 19 years
d. 25 years
Explanation:
The number of years, n is calculated for each future value as follows :
a. $1,360
Pv = - $1,000
Pmt = $ 0
P/y = 1
r = 8 %
Fv = $1,360
n = ?
Using a Financial Calculator, the number of years, n is 3.9953 or 4 years
b. $2,720
Pv = - $1,000
Pmt = $ 0
P/y = 1
r = 8 %
Fv = $2,720
n = ?
Using a Financial Calculator, the number of years, n is 13.00 or 13 years
c. $4,316
Pv = - $1,000
Pmt = $ 0
P/y = 1
r = 8 %
Fv = $4,316
n = ?
Using a Financial Calculator, the number of years, n is 19.00 or 19 years
d. $6,848
Pv = - $1,000
Pmt = $ 0
P/y = 1
r = 8 %
Fv = $6,848
n = ?
Using a Financial Calculator, the number of years, n is 24.9991 or 25 years
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Answer:
Shift outwards.
Explanation:
The production possibilities frontier or curve is the curve that shows various combinations or bundles of goods that an economy produces by using its all resource and if there is any point inside the curve then it will depict the inefficiency or underutilization of resources. Moreover, the PPF curve shifts outwards when there is an improvement in technology, due to which the output has increased. Similarly, the increase in output due to labor productivity will result in the rightward shift in the PPF curve.
Simplifying
(2a + 5)(3a + -4) = 0
Reorder the terms:
(5 + 2a)(3a + -4) = 0
Reorder the terms:
(5 + 2a)(-4 + 3a) = 0
Multiply (5 + 2a) * (-4 + 3a)
(5(-4 + 3a) + 2a * (-4 + 3a)) = 0
((-4 * 5 + 3a * 5) + 2a * (-4 + 3a)) = 0
((-20 + 15a) + 2a * (-4 + 3a)) = 0
(-20 + 15a + (-4 * 2a + 3a * 2a)) = 0
(-20 + 15a + (-8a + 6a2)) = 0
Combine like terms: 15a + -8a = 7a
(-20 + 7a + 6a2) = 0
Solving
-20 + 7a + 6a2 = 0
Solving for variable 'a'.
Factor a trinomial.
(-5 + -2a)(4 + -3a) = 0
Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve:
Simplifying
-5 + -2a = 0
Solving
-5 + -2a = 0
Move all terms containing a to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -2a = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -2a = 0 + 5
-2a = 0 + 5
Combine like terms: 0 + 5 = 5
-2a = 5
Divide each side by '-2'.
a = -2.5
Simplifying
a = -2.5
Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve:
Simplifying
4 + -3a = 0
Solving
4 + -3a = 0
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + -3a = 0 + -4
Combine like terms: 4 + -4 = 0
0 + -3a = 0 + -4
-3a = 0 + -4
Combine like terms: 0 + -4 = -4
-3a = -4
Divide each side by '-3'.
a = 1.333333333
Simplifying
a = 1.333333333
Solution
a = {-2.5, 1.333333333}