Bob and Alice want to remodel their bathroom in 4 years. They estimate the job will cost $35,000. How much must they invest now at an annual interest rate of 4% compounded quarterly to achieve their goal? The Morenos invest $9000 in an account that grows to $11,000 in 4 years. What is the annual interest rate r if interest is compounded a. Quarterly
b. Continuously
A) a. 2.192% b.2.179%
B) a. 4.5432% b.4.5153%
C) a. 6.0576% b. 6.0204%
D) a. 5.048% b.5.017%

Bob and Alice want to remodel their bathroom in 4 years. They estimate the job will cost $35,000. How much must they invest now at an annual interest rate of 4% compounded quarterly to achieve their goal?

we need to use the present value formula:

present value = future value / (1 + interest rate)ⁿ = $35,000 / (1 + 1%)¹⁶ = $29,848.74

The Morenos invest $9000 in an account that grows to $11,000 in 4 years. What is the annual interest rate r if interest is compounded

a. Quarterly

$9,000 = $11,000 / (1 + r)¹⁶

(1 + r)¹⁶ = $11,000 / $9,000 = 1.2222

¹⁶√(1 + r) = ¹⁶√1.2222

1 + r = 1.01262

r = 0.01262 = 1.26% ⇒ quarterly interest rate

annual interest rate = 1.26% x 4 = 5.048%

b. Continuously

future value = present value x eᵃⁿ

$11,000 = $9,000 x 2.718⁴ⁿ

2.718⁴ⁿ = $9,000 / $11,000 = 0.818181818

⁴√2.718⁴ⁿ  =  ⁴√0.818181818

2.718ⁿ = 0.95107

nlog2.718 = log0.95107

n 0.434249452 = -0.021787543

n = -0.021787543 / 0.434249452 = -0.05017, since n must be positive, then

n = 0.05017 = 5.017%

D) a. 5.048%    b. 5.017%

the correct answer is:

it required the president to inform congress within forty-eight hours of any new troop commitment.

the war powers resolution (1973) is a federal law designed to limit the u.s. president’s ability to initiate or intensify military actions abroad without the approval of the congress.

it establishes that the president can send armed forces into action abroad only by declaration of war by congress, statutory authorization, or in case of a national emergency created by attack upon the united states, its territories or possessions, or its armed forces.

it requires the president to notify congress within 48 hours of sending armed forces to military action.

muslims control the north africa during the period of 1500 up

to 1800. they made a barrier to prevent further european exploration from

entering the africa from the north. however, the dutch ware still able to move

toward the interior with having south africa as one of the routes leading to

the east for trading with asia.