The formula for computing compound interest for a principal P that is invested at an annual rate r and compounded annually is given by A = P(1 + r)n ,

The formula for computing compound interest for a principal P that is invested at an annual rate r and compounded annually is given by A = P(1 + r)n , where A is the accumulated amount in the account after n years. Let’s try a different approach. Substitute the value of 2 for n and solve this formula for r. Verify that you get the following result:
r = PA −1 (Hint: First solve for (1 + r)2 and then take the square root of both sides of the equation.) Notice that you now have a radical expression to work with. Substitute
$5000 for P and $5600 for A (which is the principal plus $600 in interest) to see what your rate must be. Round your answer to the nearest percent.

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  1. Step-by-step explanation:

    ONLY THE "TRUE" OPTIONS ARE LISTED BELOW

    1.)Only compound interest has an exponent in its formula(TRUE)

    ((P*(1+i)^n) - P),

    where P is the principal, i is the annual interest rate, and

    n is the number of periods which is the exponential

    2.)Compound interest earns more money than simple interest at the same rate for the same amount of time.(TRUE)

    This is true because compound interest encompass simple interest in it's formula

    3.)Simple interest is only earned on the original principal investment. (TRUE)

    4.)Compound interest is earned on principal and interest.( TRUE)

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  3. The true statements are in bold :

    1. Only compound interest has an exponent in its formula. TRUE

    The formula for compound interest is : [tex]A=P(1+\frac{r}{n})^{t}[/tex]

    The formula for simple interest is : [tex]SI=\frac{P*R*T}{100}[/tex]

    We can see the exponential power in compound interest formula.

    2. Simple interest is earned on principal and interest. FALSE (SI is earned only on principal.)

    3. Compound interest earns more money than simple interest at the same rate for the same amount of time. TRUE (This is clear with the formula given above)

    4. Simple interest earns more money than compound interest at the same rate for the same amount of time. FALSE

    5. Simple interest is only earned on the original principal investment. TRUE

    6. Only compound interest earns the same interest amount every year. FALSE

    7. Simple interest uses time in its formula. FALSE (both the formulas use time)

    8. Compound interest is earned on principal and interest. TRUE

  4. Only compound interest has an exponent in its formula.

    Simple interest is only earned on the original principal investment.

    Compound interest is earned on principal and interest.

    Step-by-step explanation:

  5. 9514 1404 393

    r ≈ 6%

    Step-by-step explanation:

    Solving for r when n=2, we have ...

      [tex]A=P(1+r)^2\\\\\dfrac{A}{P}=(1+r)^2\\\\\sqrt{\dfrac{A}{P}}=1+r\\\\\boxed{r=\sqrt{\dfrac{A}{P}}-1}[/tex]

    For the given values of A and P, the value of r is ...

      [tex]r=\sqrt{\dfrac{5600}{5000}}-1=\sqrt{1.12}-1\approx 1.0583-1\\\\\boxed{r\approx 6\%}[/tex]

  6. Step-by-step explanation:

    We would apply the formula for determining compound interest which is expressed as

    A = P(1+r/n)^nt

    Where

    A = total amount in the account at the end of t years

    r represents the interest rate.

    n represents the periodic interval at which it was compounded.

    P represents the principal or initial amount deposited

    From the information given,

    P = ₹256

    r = 100% = 100/100 = 1

    n = 4 because it was compounded 4 times in a year.

    t = 1 year

    Therefore,

    A = 256(1 + 1/4)^4 × 1

    A = 256(1 + 0.25)^4

    A = 256(1.025)^4

    A = ₹283

    The compound interest is

    283 - 256 = ₹27

  7. Only compound interest has an exponent in its formula.Simple interest is only earned on the original principal investment. Compound interest is earned on principal and interest.

    Step-by-step explanation:

    The above statements are self-explanatory.

    __

    The one statement that can be argued is ...

      "Compound interest earns more money than simple interest at the same rate for the same amount of time."

    This is true for time periods longer than the initial compounding interval. If interest is compounded annually, the amount of simple interest and compound interest will be the same for the first year. After that, the compound interest account earns more, because interest is paid on interest and principal, not just principal.

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