Mathematics: F$1,000 is deposited in a certain bank account and remains in the account along with any accumulated interest, the dollar amount of interest, i, earned by the deposit in the first n years is given by the formula i = 1,000 ( (1 + r/100)^n - 1 ), where r percent is the annual interest rate paid by the bank. is the annual interest rate paid by the bank greater than 8 percent? (1) the deposit earns a total of $210 in interest in the first two years. (2) ( 1 + r/100 )^2 1.5

202.9Step-by-step explanation: khan...

F$1,000 is deposited in a certain bank account and - id10002011690, ilvvsShatalov2214

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01.01.2022

(1) The annual interest rate is 10%, that is greater than 8%

(2) The annual interest is bigger than 22.47% and that is greater than 8%

Step-by-step explanation:

We have the equation:

$I=1,000((1+\frac{r}{100} )^{n} -1)$

Where I is the earns in interest, n is the number of years and r is the annual interest rate.

For the first case, we can replace I by $210 and n by 2 as:

$210=1,000((1+\frac{r}{100} )^{2} -1)$

Solving for r, we get:

$\frac{210}{1,000} = (1+\frac{r}{100})^{2} -1$

$0.21 +1 = (1+\frac{r}{100})^{2}$

$1.21 = (1+\frac{r}{100})^{2}$

$\sqrt{1.21} = 1 + \frac{r}{100}$

$\sqrt{1.21} - 1 = \frac{r}{100}$

$(\sqrt{1.21} - 1)100=r$

10=r

So, for the first case, the interest rate paid by the bank is 10% and it is greater than 8%

For the second case, we need to take the equation and solve for r as:

$(1+\frac{r}{100} )^{2} 1.5$

$1+\frac{r}{100} \sqrt{1.5}$

$\frac{r}{100} \sqrt{1.5}-1$

$r (\sqrt{1.5}-1)*100$

r 22.47

So, for the second case the rate need to be bigger than 22.47% and that is bigger than 8%

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