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crimeas [40]
3 years ago
8

A man invests $2000 in an account that pays 6.5% interest per year, compounded quarterly.

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
5 0

Answer:

The correct answer is a. $2275.28; b. 17.04 years

Step-by-step explanation:

Principal to be invested is $2000

Interest rate (r) per year is 6.5 quarterly.

Interest is calculated compoundly.

a. Time (t) for the investment is given to be 2 years.

Amount after two years is = Principal × ( 1+ \frac{r}{100n}) ^ {nt} where the value of n is 4.

⇒ A = 2000  × ( 1+ \frac{6.5}{400}) ^ {8}

⇒ A = $2275.28.

b. Now the value of A is given to be triple the principal = $ (3 × 2000).

Therefore we need to find the value of t.

⇒ 3 × 2000 =  2000  × ( 1+ \frac{6.5}{400}) ^ {4t}

⇒ ㏑ 3 = 4t × ㏑ ( 1.01625)

⇒ t = 17.04

Therefore it would take 17.04 years for the principal to triple.

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Please answer fast
dsp73

Answer:

A haircut costs $31

Coloring hair costs $93

Step-by-step explanation:

h = haircut

c = color

First equation: 1h + 2c = 217

Second equation: 2h + 1c = 155

Solve using elimination:

First, multiply both the equations so that they cancel the h's out:

First equation:

-1(2h + 1c = 155)

-2h - 1c = -155

Second equation:

2(1h + 2c = 217)

2h + 4c = 434

Then, put the equations together, and solve:

2h + 4c = 434

-2h - 1c = -155

3c = 279

c = 93

Find h:

2h + 1c = 155

2h + 1(93) = 155

2h + 93 = 155

2h = 62

h = 31

Hope this helped!

5 0
3 years ago
1.) Given : S is the midpoint of RT; PR = PT
garik1379 [7]

Answer: 1.

Given: S is the midpoint of RT

PR=PT

To Prove: PRS=PTS

Step-by-step explanation:

If PR=PT in a triangle PRT, then the triangle is isosceles triangle.

Therefore,  ∠PRT=∠PTR (opposite angles of an isosceles triangle are equal)

In ▲PRS and ▲PTS

PR=PT

∠PRT=∠PTR

PS=PS (PS is common)

therefore, ▲PRS≅▲PTS

Therefore, ∠PRS=∠PTS

Hence proved.

Answer: 2.

Given: E is the midpoint of AB and CD.

To Prove: AEC=BED

Step-by-step explanation:

If AB and CD are the diagonals of rectangle, then

diagonals AB=CD,  sides AC=BD and AD=BC

In ▲AEC and ▲BED,

∠AEC=∠BED(vertically opposite angles)

AE=BE

AC=BD

therefore, ▲AEC≅▲BED

Therefore,  ∠AEC=∠BED

Hence Proved.

4 0
3 years ago
-18>1.5q solve the inequality. Graph the solution.
inysia [295]

Answer:

q < - 12

Step-by-step explanation:

1.5q < - 18

4 0
3 years ago
Find the missing side
ANEK [815]

Answer:

103 degrees

Step-by-step explanation:

Right triangles interior sum will always be 180 and 44+33=77 and

180-77=103

8 0
3 years ago
A triangle has a height that is 5 units shorter than its base. If b represents the base and h represents the
11111nata11111 [884]

Answer: A = (b²-5b)/2

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

Base =b

Height = h = b-5 (the height is 5 units shorter than the base)

Since:

Area of a triangle (A)= (base x height) ÷ 2

Replacing with the values given:

A = [b (b-5)] ÷2

A = (b²-5b)/2

Feel free to ask for more if needed or if you did not understand something.

3 0
3 years ago
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