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Fudgin [204]
3 years ago
13

Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.

Mathematics
1 answer:
anzhelika [568]3 years ago
6 0
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
V_{0} =(1+ i_{a} ) ^{1}
Where
V_{0} = initial investment.
i_{a} = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
V_{0} =(1+ i_{q} ) ^{4}
Where
V_{0} = initial investment.
i_{q} = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
(1+ i_{a} )=(1+ i_{q} ) ^{4}
Notice that we are not using the initial investment V_{0} since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
(1+0.07)=(1+ i_{q} ) ^{4}
1.07=(1+ i_{q} ) ^{4}
\sqrt[4]{1.07} =1+ i_{q}
 i_{q} = \sqrt[4]{1.07} -1
i_{q} =0.017
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.


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Seamstress Jane has purchased 50 yards of red fabric and 110 yards of gold fabric to make red and gold curtains. What is the lar
Alisiya [41]

Answer: There are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.

There are 5 red fabrics and 11 gold fabrics that would be used for each curtain.

Step-by-step explanation:

Since we have given that

Number of yards of red fabric purchased by Jane = 50

Number of yards of gold fabric purchased by Jane = 110

We need to find the largest number of curtains she can make if she wants all the curtains to be exactly the same length.

For this we will find H.C.F. of 50 and 110.

Factors of 50 = 1, 2, 5, 10, 25, 50.

Factors of 110 = 1, 2, 5, 10, 11, 22, 55, 110.

So, Highest common factor of 50 and 110 is 10.

So, there are 10 largest number of curtains she can make if she wants all the curtains to be exactly the same length.

Number of yards of red fabric is given by

\frac{50}{10}=5

Number of yards of gold fabric is given by

\frac{110}{10}=11

Hence, there are 5 red fabrics and 11 gold fabrics that would be used for each curtain.

4 0
3 years ago
29+d = 54; 24, 25, 26
Anna11 [10]

Answer:

25

Step-by-step explanation:

54 minus 29 is 25

5 0
3 years ago
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Paul can install a 300 hundred square foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long wou
Vadim26 [7]
ANSWER

Paul and Matt will take
9.9 \: \: hours
to install the floor working together.

EXPLANATION

First, calculate Paul's rate, which is

= \frac{1}{18}

Next, calculate Matt's rate, which is,
= \frac{1}{22}

Let us assume that, Paul and Matt took
x \: hours
to do the work together.

Then, the rate of working together is,

= \frac{1}{x}

Now, add the individual rates and equate to the rate of working together to form an equation that will help us solve for x.

\frac{1}{18} + \frac{1}{22} = \frac{1}{x}

Simplify the left hand side

\frac{11 + 9}{198} = \frac{1}{x}

\frac{20}{198} = \frac{1}{x}

We reciprocate both sides to get (You could have also done cross multiplication).

\frac{198}{20} = \frac{x}{1}

x = 9.9 \: hours
7 0
3 years ago
Help me with this very pls. I will give you the brainliest and a thanks!! :)) Can you do 1 and 4 thanks!! :)))
lubasha [3.4K]
Answer: 1. 12 and 4 I think
4 0
3 years ago
ASAP NO WORK JUST ANSWER
Hunter-Best [27]

Answer:

c

Step-by-step explanation:

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