At the end of 2​ years, P dollars invested at an interest rate r compounded annually increases to an​ amount, A​ dollars, given by the follo

Question

At the end of 2​ years, P dollars invested at an interest rate r compounded annually increases to an​ amount, A​ dollars, given by the following formula. Upper A equals Upper P (1 plus r )squared Find the interest rate if ​$100 increased to ​$196 in 2 years. Write your answer as a percent.

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Kylie 1 week 2022-01-07T06:55:43+00:00 1 Answer 0 views 0

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    2022-01-07T06:56:58+00:00

    Answer:

    40%.

    Step-by-step explanation:

    We have been given that an amount of $100 compounded annually is increased to ​$196 in 2 years. We are asked to find the interest rate.

    We will use compound interest formula to solve our given problem.

    A=P(1+\frac{r}{n})^{nt}, where,

    A = Final amount,

    P = Principal amount,

    r = Annual interest rate in decimal form,

    n = Number of times interest is compounded per year,

    t = Time in years.

    Upon substituting our given values in above formula, we will get:

    196=100(1+\frac{r}{1})^{1*2}

    196=100(1+r)^{2}

    \frac{196}{100}=\frac{100(1+r)^{2}}{100}\\\\1.96=(1+r)^2

    (1+r)^2=1.96

    Take positive square root of both sides:

    \sqrt{(1+r)^2}=\sqrt{1.96}

    1+r=1.4\\\\1-1+r=1.4-1\\\\r=0.4

    Since interest rate is in decimal, form, so we will convert it into percentage as:

    0.4\times 100\%=40\%

    Therefore, the interest rate was 40%.

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