Ivan put 500 000ISK (Icelandic Krona) and Blake put 700 000ISK into savings accounts
at different banks.
After 8 years, Ivan and Blake have the same amount of money in their accounts.
They both receive interest compounded quarterly and Blake has an annual interest rate
that is half of Ivan's annual interest rate.
Work out the annual interest rate that Blake receives.

Answers

Answer 1

Using compound interest, it is found that Blake receives an annual rate of 4.27%.

Compound interest:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

A(t) is the amount of money after t years.  P is the principal(the initial sum of money).  r is the interest rate(as a decimal value).  n is the number of times that interest is compounded per year.  t is the time in years for which the money is invested or borrowed.

Ivan's parameters are given by:

Put 500 000 ISK, hence [tex]P = 500000[/tex]8 years, hence [tex]t = 8[/tex]Quarterly compounding, hence [tex]n = 4[/tex]Interest rate of r.

Hence:

[tex]A_i(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A_i(t) = 500000\left(1 + \frac{r}{4}\right)^{32}[/tex]

[tex]A_i(t) = 500000(1 + 0.25r)^{32}[/tex]

Blake's parameters are given by:

Put 700 000 ISK, hence [tex]P = 700000[/tex]8 years, hence [tex]t = 8[/tex]Quarterly compounding, hence [tex]n = 4[/tex]Interest rate that is half of Ivan's, hence [tex]\frac{r}{2}[/tex]

Thus:

[tex]A_b(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A_b(t) = 700000(1 + 0.125r)^{32}[/tex]

These amounts are equal, hence:

[tex]A_i(t) = A_b(t)[/tex]

[tex]500000(1 + 0.25r)^{32} = 700000(1 + 0.125r)^{32}[/tex]

[tex]\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32} = \frac{700000}{500000}[/tex]

[tex]\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32} = \frac{7}{5}[/tex]

[tex]\sqrt[32]{\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32}} = \sqrt[32]{\frac{7}{5}}[/tex]

[tex]\frac{1 + 0.25r}{1 + 0.125r} = \left(\frac{7}{5}\right)^{\frac{1}{32}}[/tex]

[tex]\frac{1 + 0.25r}{1 + 0.125r} = 1.01057023172 [/tex]

[tex]1 + 0.25r = 1.01057023172 + 0.12632127896r[/tex]

[tex]0.12367872103r = 0.01057023172 [/tex]

[tex]r = \frac{0.01057023172}{0.12367872103}[/tex]

[tex]r = 0.0854[/tex]

Blake's rate is:

[tex]\frac{r}{2} = \frac{0.0855}{2} = 0.0427[/tex]

Blake receives an annual rate of 4.27%.

A similar problem is given at https://brainly.com/question/24507395


Related Questions

Christine's parents gave her $70 to spend at the Topsfield Fair. She spent $10 on flowers and needs to buy vases. Each antique flower vase at the fair costs $3.
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at least 20 vases
O at the most 20 vases
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97

Step-by-step explanation:

Which circle has a radius that measures 10 units?
10
D
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OG
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Answers

Circle F 20
Hope this helps :))

Option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

What is Circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

The distance across a circle through the centre is called the diameter.

Diameter = 2 × radius

In the given figures, option B has a diameter of 20

so radius = diameter /2

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=10 units

Hence, option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

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f(x)=3x+5 and g(x)=2x+1

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Answers

You can treat x and 2x+1 just as though they are real numbers.

So f(2x+1) = 3(2x+1) - 5 = 6x + 3 - 5 = 6x - 2

In the above, I made use of something called the distributive law which says that if a,b and c are real numbers, then a(b+c) = ab + ac.

Suppose that you randomly selected 22 adults. If 10% of the population smoke, a) Using the Range Rule of Thumb, what is the minimum number of usual smokers we can expect to get out of 22 adults?

Answers

Answer: 2 to 3 people who would be smoking

Step-by-step explanation:

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Answers

Answer:

8 months

Step-by-step explanation:

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49/72 is the correct answer!

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Rule for function

If Domains of relation have unique Range then it's function otherwise not a function.

Now

FunctionFunctionRelation/Not a functionNot a function/Relation

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Answers

Answer:(5x+8)/[(x+4)(x-1)(x+3)]

Step-by-step explanation:

1. First factorize the quad expressions in the denomeneter of both fractions.

2. Then choose you arithmetic common denomeneter .

3. And the rest is child's play.

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Answers

Answer:

5a (a -2)

Step-by-step explanation:

Hey there,

Here, you have to get the common factors out from the brackets.

According to this question,

a and 5 are the common factors.

Therefore, you can write the answer like this,

5a² - 10a

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Hope this helps you.

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Answers

Answer:

Obtuse or right angle

Step-by-step explanation:

Also you should stop making your question worth so many points

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Answers

Answer: where is the question??

what do you need help with?

Trust Officer Megan is the trust officer for an estate. If she
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Answer:

????????

Step-by-step explanation:

i don't know if I can help with the subject line

In the average household, the tv is on for 6. 75 hours a day. How many hours will have passed after 77. 7 years?.

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the answer is 524.47500

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The ANSWER is m = n - L

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Answer: its 6

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How will knowing the value for the best measure of center for the heights of the adult males help Nancy determine whether she can send the same distributions of sizes to each country for the men’s clothing line or will need to adjust the distributions she sends?

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The best measure of center for the heights help Nancy to determine the sizes of cloth for countries, as it does not include outliers

What is mean of the data set?

The mean of the data is the average value of the given data. The mean of the data is the ratio of the sum of all the values of data to the total number of values of data.

The mean of the data is the center tendency and includes the outlines.

The value for the best measure of center for the heights of the adult males help can help Nancy in two ways:

She can send the same distributions of sizes to each country for the men’s clothing line She needs to adjust the distributions she sends.

Here, when Nancy uses the mean of the data of height, she also measures the outliers. This affect the calculation of her. With the best measure of center, help her to deter line the size.

Thus, the best measure of center for the heights help Nancy to determine the sizes of cloth for countries, as it does not include outliers.

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Explain what the point (6,2) represents.

Answers

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Answers

Answer:

x = 2

Step-by-step explanation:

Given:

y = -2x + 7 y = 5х – 7

If y = -2x + 7 and y = 5х – 7, then -2x + 7 = 5х – 7. Now, let's solve.

=> -2x + 7 = 5х – 7

=> 7x = 14

=> x = 2

Since we found 'x', let's find 'y' with the given clue using one equation among any of the two equations.

=> y = 5х – 7

=> y = 5(2) - 7

=> y = 10 - 7

=> y = 3

Hoped this helped.

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Answers

Answer:

Its D.

Step-by-step explanation:

The 3 as the exponent makes it cubic and since the x+1 is in parenthesis you would move it 1 unit to the left

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Answers

Answer:

100,000 × 1,000,000 = 1.E11

Answer:

100000000000

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

EX: 3*4=12

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Answers

Answer:

a = 7

Step-by-step explanation:

Equation of line : y = mx + b

m = slope

Plug in coordinates:  

Slope = Change in y/Change in X

Slope = 13-4/5-2 = 9/3 = 3

Plug in coordinates:

y - intercept = b

13 = 5(3) + b

13 = 15 + b

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Equation: y = 3x - 2

Input 3 for x

y = 3x - 2

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y = 7

-Chetan K

Find the perimeter. Simplify your answer.

Answers

perimeter= 4p+5 + 10 + 8
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please helpppppppppoppo

Answers

Step-by-step explanation:

360_90_110=1602a+3a=160a=32°

Find the slope of line 2, which is parallel to line 1. Line i goes through the points
(-13, -6), (7, 15).

Answers

(-13, -6), (7, 15) = 1.05

Equation: y = 1.05x + 7.65.

The entered points belong to an increasing, linear function.

Answer:

m = rise / run = 21/20, or m = 1.05

Step-by-step explanation:

If the lines are parallel, their slopes are identical.  So we can find the slope of line 1 and know that it's also the slope of line 2.

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Answers

Answer:

8, 13, 18

Step-by-step explanation:

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what are the values of each variable

Answers

Answer:

x=14

Step-by-step explanation:

2x+4=3x-10

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x=14

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Annie bakes cookies and cupcakes in a ratio of 5 to 1 for her gift boxes. Her school needs 36 desserts to sell in a bake sale. How many cupcakes will she bake? How many cookies will she bake? Explain your answers.

Answers

Answer:

30 cookies and 6 cupcakes

Step-by-step explanation:

5+1=6

5:1=6

?:?=36

36/6=6

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30 cookies

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100 points if u get this right ty have a nice day !

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Answer:

its 32 yards if I'm correct

Step-by-step explanation:

I'm not for sure but I remember doing something like this

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