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If $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 \small I = 1,000 \left (\left (1+\frac{r}{100} \right )^{n}-1 \right ) , 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?

Sagot :

MrRoyal

Answer:

The rate is greater than 8%

Explanation:

Given

[tex]\small I = 1,000 \left (\left (1+\frac{r}{100} \right )^{n}-1 \right )[/tex]

Missing part of question

[tex]I =210[/tex]

[tex]n =2[/tex]

Required

Is r > 1

We have:

[tex]\small I = 1,000 \left (\left (1+\frac{r}{100} \right )^{n}-1 \right )[/tex]

Substitute values for r and I

[tex]210 = 1,000 \left (\left (1+\frac{r}{100} \right )^{2}-1 \right )[/tex]

Divide both sides by 1000

[tex]0.210 = \left (\left (1+\frac{r}{100} \right )^{2}-1 \right )[/tex]

Add 1 to both sides

[tex]1.210 = (1+\frac{r}{100} \right ))^{2}[/tex]

Take square roots of both sides

[tex]\sqrt{1.210} = 1+\frac{r}{100}[/tex]

[tex]1.1 = 1+\frac{r}{100}[/tex]

Subtract 1 from both sides

[tex]0.1 = \frac{r}{100}[/tex]

Multiply both sides by 100

[tex]r = 10[/tex]

[tex]10 > 8[/tex]

Hence, the rate is greater than 8%

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