The amount of simple interest is calculated by which of the following formulas? $\newline$ $a. \quad \text{Interest} = P \cdot r \cdot t$ $\newline$ $b. \quad \text{Interest} = (\frac{r}{n}+1)^{t}$ $\newline$ $c. \quad \text{Interest} = (1+\frac{r}{n})^{nt}$ $\newline$ $d. \text{Interest} = (1+\frac{r}{n})^{nt}$ $\newline$ $e. \text{Interest} = P \cdot r \cdot t$ $\newline$

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Q. The amount of simple interest is calculated by which of the following formulas?

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a. \quad \text{Interest} = P \cdot r \cdot t

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b. \quad \text{Interest} = (\frac{r}{n}+1)^{t}

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c. \quad \text{Interest} = (1+\frac{r}{n})^{nt}

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d. \text{Interest} = (1+\frac{r}{n})^{nt}

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e. \text{Interest} = P \cdot r \cdot t

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Identify Formula for Simple Interest: To find the correct formula for calculating simple interest, we need to identify the formula that represents the relationship between the principal amount $P$ , the rate of interest $r$ , and the time $t$ for which the interest is calculated. Simple interest is calculated without compounding, meaning that the interest is not reinvested to earn additional interest.
Eliminate Incorrect Options: Looking at the given options, we can eliminate options b and d because they involve compounding, which is not a characteristic of simple interest. Option a has the formula Interest $= P/r\ast t$ , which seems incorrect because the rate $r$ should be multiplied, not divided. Therefore, option c, Interest $= P\ast r\ast t$ , is the correct formula for simple interest because it multiplies the principal amount by the rate and the time.
Calculate Permutations for Swimmers: Now, to determine the number of different ways ten swimmers can finish the race, we need to calculate the number of permutations of ten distinct swimmers. This is because the order in which they finish matters.
Calculate $10$ Factorial: The number of permutations of $n$ distinct objects is given by $n!$ , where ＂!＂ denotes factorial. Therefore, the number of different ways ten swimmers can finish the race is $10!$ ( $10$ factorial).
Calculate $10$ Factorial: The number of permutations of $n$ distinct objects is given by $n!$ , where ＂!＂ denotes factorial. Therefore, the number of different ways ten swimmers can finish the race is $10!$ ( $10$ factorial).Calculating $10$ factorial, we have $10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ .
Calculate $10$ Factorial: The number of permutations of $n$ distinct objects is given by $n!$ , where ＂!＂ denotes factorial. Therefore, the number of different ways ten swimmers can finish the race is $10!$ ( $10$ factorial).Calculating $10$ factorial, we have $10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ .Performing the multiplication, we get $10! = 3,628,800$ .