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Question

Answers

A. Rs. 8820

B. Rs. 8020

C. Rs. 8780

D. Rs. 7820

Answer
Verified

Hint:- Directly use compound interest formula i.e. \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\] to get the amount Maria has after the second year. For two years take n as 2 .

Complete step-by-step answer:

As we know that the principal amount is Rs. 8000.

Rate of interest is 5% at annual rate.

And the rate of interest is compounded annually.

So, now we can apply compound interest formulas to find the amount after the second year.

According to compound interest formula compound interest for t years is calculated as \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\]where r is the annual rate of interest, t will be number of years after which we had to find the amount, P will be the principal amount and A will be the amount after t years.

So, according to the question,

P = Rs. 8000

r = 5%

and t = 2 years.

So, putting all the values in the formula of compound interest we will get,

\[A = 8000{\left( {1 + \dfrac{5}{{100}}} \right)^2} = 8000{\left( {\dfrac{{105}}{{100}}} \right)^2}\]

So, \[A = 8000 \times \dfrac{{105}}{{100}} \times \dfrac{{105}}{{100}} = \dfrac{{8 \times 105 \times 105}}{{10}} = 8820\]

Hence, the amount credited against Maria's name for two years will be equal to Rs. 8820.

Hence, the correct option will be A.

Note:- Whenever we come up with this type of question, we should note that when we are given the question that the interest is compounded then we add only compound interest formulas. And simple interest and compound interest are not the same because simple interest is based on the principal amount of a loan or deposit. But in contrast, compound interest is based on the principal amount and the interest that accumulates on it every period. So, we had to put values in the compound interest formula i.e. \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\] (where A is the amount invested, r is the rate of interest annually and t will be the total number of years) to get the amount of money credited against Maria name after two years (A). This will be the easiest and efficient way to find the solution of the problem.

Complete step-by-step answer:

As we know that the principal amount is Rs. 8000.

Rate of interest is 5% at annual rate.

And the rate of interest is compounded annually.

So, now we can apply compound interest formulas to find the amount after the second year.

According to compound interest formula compound interest for t years is calculated as \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\]where r is the annual rate of interest, t will be number of years after which we had to find the amount, P will be the principal amount and A will be the amount after t years.

So, according to the question,

P = Rs. 8000

r = 5%

and t = 2 years.

So, putting all the values in the formula of compound interest we will get,

\[A = 8000{\left( {1 + \dfrac{5}{{100}}} \right)^2} = 8000{\left( {\dfrac{{105}}{{100}}} \right)^2}\]

So, \[A = 8000 \times \dfrac{{105}}{{100}} \times \dfrac{{105}}{{100}} = \dfrac{{8 \times 105 \times 105}}{{10}} = 8820\]

Hence, the amount credited against Maria's name for two years will be equal to Rs. 8820.

Hence, the correct option will be A.

Note:- Whenever we come up with this type of question, we should note that when we are given the question that the interest is compounded then we add only compound interest formulas. And simple interest and compound interest are not the same because simple interest is based on the principal amount of a loan or deposit. But in contrast, compound interest is based on the principal amount and the interest that accumulates on it every period. So, we had to put values in the compound interest formula i.e. \[A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}\] (where A is the amount invested, r is the rate of interest annually and t will be the total number of years) to get the amount of money credited against Maria name after two years (A). This will be the easiest and efficient way to find the solution of the problem.

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