According to the compound interest model, we find the following results: I) x ≈ 11.5 yr, C' = $ 101317.36, II) r ≈ 7.4 %, x ≈ 9.8 yr, III) C = $ 7626.38, x ≈ 8.6 yr, IV) r ≈ 6.5 %, C = $ 12801.61

<h3>How to determined all the variables associated with compound interest</h3>

Compound interest describes the capital gain in term of deposited capital and the consideration that such capital is increased continuously in time. The compound interest model is shown below:

C' = C · (1 + r/100)ˣ (1)

Where:

C - Initial capital
C' - Current capital
r - Interest rate, in percentage.
t - Time, in years

The doubling time (x) is the period needed for a capital to be doubled. It is described by the following expression based on (1):

x = (㏒ 2)/[㏒ (1 + r/100)] (2)

Now we proceed to calculate each missing variable:

Case I - Doubling time

x = (㏒ 2)/[㏒ (1 + 6.2/100)]

x ≈ 11.5

Case I - Current capital

C' = 75000 · (1 + 6.2/100)⁵

C' = 101317.36

Case II - Interest rate

$r = 100\cdot \left(\sqrt [5] {\frac{7130.90}{5000} }-1\right)$

r ≈ 7.4

Case II - Doubling time

x = (㏒ 2)/[㏒ (1 + 7.3/100)]

x ≈ 9.8

Case III - Initial capital

C = 11414.71/(1 + 8.4/100)⁵

C = 7626.38

Case III - Doubling time

x = (㏒ 2)/[㏒ (1 + 8.4/100)]

x ≈ 8.6

Case IV - Interest rate

$r = 100\cdot \left(\sqrt [11] {2 }-1\right)$

r ≈ 6.5

Case IV - Initial capital

C = 17539.32/(1 + 6.5/100)⁵

C = 12801.61

To learn more on compound interest: brainly.com/question/14295570

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3 0

2 years ago

A car is traveling at a speed of 55 mph. You want to write an algebraic expression to show how far the car will travel in a cert

WARRIOR [948]

distance = rate * time.

distance is number of miles the car has traveled.

rate = number of miles per hour the car is traveling at.

time = number of hours the car has been driven.

let D = distance.

let T = time.

let R = rate

the general equation is D = R*T

as long as the car will always be driven at 55 miles per hour, you can substitute 55 for R and that becomes your constant.

The equation then becomes D = 55 * T.

example:

you drive 5 hours.

D = 55 * T = 55 * 5 = 275 miles.

If you drive at 55 miles per hour for 5 hours, you will have driven 275 miles.

Hope this helps!

4 0

4 years ago

Name the like terms is this expression: (1 Point) 9 - z + 3 – 2z ￼

Name the like terms is this expression: (1 Point) 9 - z + 3 – 2z