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 interes

Question

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%

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Ayla 1 week 2021-09-15T23:19:17+00:00 2 Answers 0

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    0
    2021-09-15T23:20:32+00:00

    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%.

    0
    2021-09-15T23:21:15+00:00

    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

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