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nlexa [21]
3 years ago
12

You decide to put $175 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate

of 3% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
Mathematics
1 answer:
myrzilka [38]3 years ago
7 0
The future value (A) of a principal amount P compounded 12 times per year at rate r for t years is given by
  A = P·(1 + r/12)^(12t)

Substitute the given values and solve for t.
  3000 = 175·(1 + .03/12)^(12t)
Taking logarithms, this becomes
  log(3000) = log(175) + 12t·log(1.0025)
  (log(3000) -log(175))/(12·log(1.0025)) = t
  t ≈ 94.84

It will take 95 years for the balance to grow by a factor of 17 to $3000.
You might be interested in
Two diameters of circle P are AB and CD. Find the measure of arc ACD and arc AC when arc AD has a measure of 20 degrees
steposvetlana [31]

Answer:

Hence measure of arc ACD and arc AC are 340 degrees and 160 degrees respectively.

Step-by-step explanation:

Given:

A Circle with p as center and AB and CD as 2 diameters for a circle.

To Find:

Measure of ACD, and arc AC when arc AD is 20 degrees.

Solution:

<em>As we know that , Diameter is biggest chord which passes through center of circle,</em>

<em>Hence it divides the circle into two equal parts and making center as midpoint of it</em> .

(Refer the attachment)

angle APD=20 degree or arc AD=20 degree.

So AB as diameter ,so  arc DB=160 degree  or BPD=160 degree as A-B-P are

and angle APD and BPC are vertical opposite angles so they are congruent BPC=20 degree

Now,

points A,C,B,D,A makes circle which measures 360 degrees.

to find ACD

measure of ACD=360-(meaure of arc AD or angle APD)

=360-20

=340 degree.

Now arc AC,

as AB is diameter with p as midpoint ,A-P-B

arc APB=180 and arc BC=20 or angle BPC=20 degrees.

For measure of arc AC= measure of arc APB- arc BC

arc AC=180-20 degrees.

arc AC=160 degrees.

5 0
3 years ago
If 5 + 20 times 2 Superscript 2 minus 3 x Baseline = 10 times 2 Superscript negative 2 x Baseline + 5, what is the value of x? –
sp2606 [1]

Answer:

<h3>Option D) 3 is correct</h3><h3>Therefore the value of x is 3</h3>

Step-by-step explanation:

Given equation is 5+20\times (2)^{2-3x}=10\times (2)^{-2x}+5

<h3>To find the value of x :</h3>

First solving the given equation we have,

5+20\times (2)^{2-3x}=10\times (2)^{-2x}+5

5+20\times (2)^{2-3x}-5=10\times (2)^{-2x}+5-5

20\times (2)^{2-3x}=10\times (2)^{-2x}

20\times (2)^2.(2)^{-3x}=10\times (2)^{-2x}

20\times 4.(2)^{-3x}=10\times (2)^{-2x}

80(2)^{-3x}=10\times (2)^{-2x}

\frac{80}{10}(2)^{-3x}=\frac{10\times (2)^{-2x}}{10}

8(2)^{-3x}=(2)^{-2x}

\frac{(2)^{-3x}}{(2)^{-2x}}=\frac{1}{8}

(2)^{-3x}.(2)^{2x}=\frac{1}{2^3} ( by using the property \frac{1}{a^{-m}}=a^m )

2^{-3x+2x}=\frac{1}{2^3} ( by using the property a^m.a^n=a^{m+n} )

2^{-x}=\frac{1}{2^3}

\frac{1}{2^x}=\frac{1}{2^3} ( by using the property a^{-m}=\frac{1}{a^m} )

Since bases are same so powers are same

Therefore we can equate the powers we get x=3

<h3>Therefore the value of x is 3</h3><h3>Option D) 3 is correct</h3>
5 0
3 years ago
Read 2 more answers
Your teacher asks you to find a recipe that includes two ingredients with a ratio of 1/2 cup/ 1/8 cup. a. give an example of two
Ksivusya [100]
A. Sugar And Brown Sugar (For Cookies)


B. No.

C 1/2 Cup (INGREDIENT) And 1/8 Cup (INGREDIENT)
7 0
3 years ago
Yolanda left for a youth retreat at 8:00 p.m. On Friday. She came home on Sunday morning at 10:00 a.m. How long was Yolanda away
weeeeeb [17]
Yolanda was gone for 12 hours 
6 0
3 years ago
Read 2 more answers
When three pipes fill a pool, they can finish in 12 hours. Two of the pipes can finish in 18 hours if they are working together.
ladessa [460]
3 pipes take 12 hours
⇒ In 1 hour, the 3 pipes can fill 1/12 of the pool

2 of the pipes take 18 hours
⇒ in 1 hour, the 2 pipes can fill 1/18 of the pool

In 1 hour, the third pipe alone can fill :

\dfrac{1}{12} - \dfrac{1}{18} = \dfrac{3}{36} - \dfrac{2}{36} = \dfrac{1}{36} \text { of the pool}

Time needed :

1 \div \dfrac{1}{36} = 1 \times 36 = 36 \text { hours}

----------------------------------------------------------------------------------------
Answer: It will take 36 hours for the third pipe to fill the pool.
----------------------------------------------------------------------------------------

5 0
3 years ago
Read 2 more answers
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