The minimum initial deposit Arthur must make is $ 4.24.
Since Arthur is saving money to buy a used car in 8 months, and the car costs $ 2,180, and Arthur plans to start with an initial deposit and then deposit 25% more than the previous month until he has enough money to buy the car, to determine what is the minimum initial deposit Arthur must make the following calculation should be performed:
- X x 1.25 x 1.56 x 1.95 x 2.44 x 3.05 x 3.81 x 4.76 = 2180
- 514.10X = 2180
- X = 2180 / 514.10
- X = 4.24
Therefore, the minimum initial deposit Arthur must make is $ 4.24.
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Step-by-step explanation:
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It appears that the Pythagorean theorem can be applied to this problem
(distance to shadow)² = (height of building)² + (length of shadow)²
(38 m)² = (height of building)² + (28 m)²
660 m² = (height of building)²
Then the height of the building is
height of building = √660 m ≈ 25.7 m
To solve this, we simply need to remember our rules about order of operations. They tell us that first, we should distribute the 2 with the rest of the parentheses.
5-2(x-3)
5-2x+6
Next, we should combine our like-terms.
5-2x+6
11-2x
Seeing as we do not know the value of the variable, the simplest form of the expression is 11-2x.
The formula for the future value A, given annual interest rate r, number of years t, and deposit amount P can be written as
... A = P(1 +r/12)((1+r/12)^(12t) -1)/(r/12)
Filling in the given numbers, you have
... A = 200(1+.0275/12)((1+.0275/12)^(12·39) -1)/(.0275/12) ≈ 167,868.30
The appropriate choice is $167,868.30.
_____
The formula is the one for the sum of a geometric series. It can be useful to consider the last deposit made as the first term of the series.
