Question

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?

Answer 1

Answer:

The rate is greater than 8%

Explanation:

Given

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

Missing part of question

$I =210$

$n =2$

Required

Is r > 1

We have:

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

Substitute values for r and I

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

Divide both sides by 1000

$0.210 = \left (\left (1+\frac{r}{100} \right )^{2}-1 \right )$

Add 1 to both sides

$1.210 = (1+\frac{r}{100} \right ))^{2}$

Take square roots of both sides

$\sqrt{1.210} = 1+\frac{r}{100}$

$1.1 = 1+\frac{r}{100}$

Subtract 1 from both sides

$0.1 = \frac{r}{100}$

Multiply both sides by 100

$r = 10$

$10 > 8$

Hence, the rate is greater than 8%