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3 years ago

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Given the equation A=250(1.1)t, you can determine that the interest is compounded annually and the interest rate is 10%. Suppose

the interest rate were to change to being compounded quarterly. Rewrite the equation to find the new interest rate that would keep A and P the same.
What is the approximate new interest rate?

Convert your answer to a percentage, round it to the nearest tenth, and enter it in the space provided, like this: 42.53%

2 answers:

Wewaii [24]3 years ago

5 0

Answer:

=250(1.025)∧4t

Step-by-step explanation:

Using the compound interest formula we can find the expression for the total amount that accumulates in the given time t.

A=P(1+R/n)ⁿᵇ

where A is the amount, P the principal amount, R the rate as a decimal n is the number of times it is compounded and b the time.

When compounded annually, the expression becomes

A=250(1.1)∧t

When compounded quarterly, we introduce the n in our expression.

A=250(1+0.1/4)∧4t

=250(1.025)∧4t

Cloud [144]3 years ago

3 0

Answer:

$A=250(1.025)^{4t}$

Step-by-step explanation:

$A=250(1.1)^{t}$

The interest rate is 10% or 0.1

n = 1

The compound interest formula is : $A=p(1+\frac{r}{n})^{nt}$

n is the number of times amount is compounded.

Lets say the interest rate were to change to being compounded quarterly.

So, here A, p will remain same, r will be divided by 4 and n will change to 4.

So, new equation will be :

$A=250(1+\frac{0.1}{4})^{4t}$

=> $A=250(1.025)^{4t}$

The approximate new interest rate will be = $10/4/100=0.025$ and in percentage it is 2.50%.

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Read 2 more answers

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cestrela7 [59]

Answer:

P (Cheese) = 0.199, P (Sausage) = 0.259, P (Pepperoni) = 0.181,

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Step-by-step explanation:

Given:

Number of students who prefer cheese = 43

Number of students who prefer sausage = 56

Number of students who prefer pepperoni = 39

Number of students who prefer supreme = 28

Number of students who prefer another kind = 31

Number of students who did not like any kind = 19

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The probability that a students likes pizza is,

$P(Student\ likes\ pizza)=\frac{No.\ of\ students\ who\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}$

$=\frac{197}{216} \\=0.912$

The probability that a students does not likes pizza is,

$P(Student\ does\ not\ likes\ pizza)=\frac{No.\ of\ students\ who\ does\ not\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}$

$=\frac{19}{216} \\=0.088$

The probability distribution of students who prefer different kinds of pizza is:

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$P(A\ Student\ prefers\ cheese)=\frac{No.\ of\ students\ who\ prefer\ cheese}{Total\ no.\ of\ students\ surveyed}$

$=\frac{43}{216}\\=0.199$

The probability that a student likes sausage:

$P(A\ Student\ prefers\ sausage)=\frac{No.\ of\ students\ who\ prefer\ sausage}{Total\ no.\ of\ students\ surveyed}$

$=\frac{56}{216}\\=0.259$

The probability that a student likes pepperoni:

$P(A\ Student\ prefers\ pepperoni)=\frac{No.\ of\ students\ who\ prefer\ pepperoni}{Total\ no.\ of\ students\ surveyed}$

$=\frac{39}{216}\\=0.181$

The probability that a student likes supreme:

$P(A\ Student\ prefers\ supreme)=\frac{No.\ of\ students\ who\ prefer\ supreme}{Total\ no.\ of\ students\ surveyed}$

$=\frac{28}{216}\\=0.130$

The probability that a student likes another kind:

$P(A\ Student\ prefers\ another\ kind)=\frac{No.\ of\ students\ who\ prefer\ another\ kind}{Total\ no.\ of\ students\ surveyed}$

$=\frac{31}{216}\\=0.144$

Thus, the probability distribution table is displayed below:

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So the numbers are 3; 4 and 5.

You can re-check your answers (very important):
3+4+5 = 12
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The answer has been approved.

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