Question

Maria invested Rs 80,000 in a business. She would be paid interest at 5% per annum compounded annually. Find (i) the amount standing to her credit at the end of the second year. (ii) The interest for the third year.

Answer 1

Hint: Here we go through by applying the formula of amount after t year at the rate of r% compound i.e. $A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^t}$ here A=amount, P=principal amount, r=rate and t=time.

Here in this question it is given that
Principal, P= Rs. 80,000
Rate of interest, r=5%
And we have to find the amount at the end of two year so t=2.
(i) The amount credited at the end of the second year, $A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^t}$
Now put the values in the formula to find the amount.
$A = 80000{\left( {1 + \dfrac{5}{{100}}} \right)^2} = 80000 \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} = 88200$
Hence, the amount standing to her credit at the end of the second year is Rs. 88200.

 Now for solving the (ii) part,
(ii) We have to first calculate the total amount in third year and then for finding the interest for third year we will subtract the amount of two years.
Here Principal, P= Rs. 80,000
Rate of interest, r=5%
And we have to find the amount at the end of three year so t=3.
The amount credited at the end of the third year, $A = P{\left[ {1 + \dfrac{r}{{100}}} \right]^t}$
$A = 80000{\left( {1 + \dfrac{5}{{100}}} \right)^3} = 80000 \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} = 92610$.
Interest of third year=Amount of three years-Amount of two years.
Interest=92610-88200 (as we find the amount for two years above).
=4410
$\therefore $ The interest for the third year is 44410. Answer

Note: Whenever we face such a type of question the key concept for solving the question is you must always remember the formula related to compound interest for solving such a type of question. By putting the given terms in formula you can easily get the answer. And for finding the interest for a specific year just subtract the amount of its previous year from the amount of that year.