Answer

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**Hint:**The given question can be solved with the help of the concept of compound interest and simple interest. You must note the 6000 Dollars is the principal amount. As well as the rate and the time period has been provided that is 1.5% and 8 years. So, let’s see what will be the approach for the given question.

**Complete Complete Step by Step Solution:**

In the given question we need to find the rate of simple interest per year that Eisha received.

We are provided with the principal amount, rate and time period, that means, we have,

Principal Amount (P) = 6000 Dollars

Rate for compound interest(r) = 1.5%

Time period (t) = 8 years

The amount considered by Compound Interest = $P{{(1+\dfrac{r}{100})}^{t}}$

Putting the required values, we get,

Compound Interest = $6000{{(1+\dfrac{1.5}{100})}^{8}}$

Now, we will solve the bracket portion first,

Compound Interest = $6000{{(\dfrac{100+1.5}{100})}^{8}}$

Compound Interest = $6000{{(\dfrac{101.5}{100})}^{8}}$

Now, when we solve the bracket again, we get,

Compound Interest = $6000{{(1.015)}^{8}}$

Compound Interest = 6758 Dollars

As the amount for simple interest and compound interest are the same.

Therefore, Compound Interest = Simple Interest, where,

Compound Interest = $P{{(1+\dfrac{r}{100})}^{t}}$ and Simple Interest = $P+(\dfrac{P\times r\times t}{100})$

As we need to find the rate we will keep it as it is and we will fill the rest of the values.

$\therefore 6758=6000[1+\dfrac{r\times 8}{100}]$

Move the 6000 to the left side, we get,

$\Rightarrow \dfrac{6758}{6000}=[1+\dfrac{r\times 8}{100}]$

Also, take the 1 to the left side, we get,

$\Rightarrow \dfrac{6758}{6000}-1=\dfrac{r\times 8}{100}$

After simplifying the above, we get,

$\Rightarrow 1.1264-1=\dfrac{8r}{100}$

$\Rightarrow 0.1264=\dfrac{8r}{100}$

Now, we will solve for rate, that means, we get,

$\Rightarrow r=\dfrac{0.1264\times 100}{8}$

$\Rightarrow r=1.58%$

**Therefore, the rate of simple interest per year that Eisha received is 1.58%**

**Note:**

In the above question, we have used the simple concept of interest that is the compound interest and simple interest. We need to keep in mind compound interest for each year the interest is different but for simple interest, it is the same for all years.

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