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Meena and Eisha both invest their $6000. Meena invests her $6000 at a rate of 1.5% per year compound interest. Eisha invests her $6000 in a bank that pays simple interest. After 8 years, their investments are worth the same amount. Calculate the rate of simple interest per year that Eisha received.

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Last updated date: 20th Jun 2024
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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.