Question

Prem lends Rs. 100,000 at C.I. for 3 years. If the rate of interest for the first two years is 15% per year and for the third year it is 16%, calculate the sum of Rohit will get at the end of the third year.
A. $Rs.155410$
B. $Rs.153410$
C. $Rs.125410$
D. $Rs.135410$

Answer 1

According to the question we have to determine the sum of Rohit will get at the end of the third year when Prem lends Rs. 100,000 at C.I. for 3 years. If the rate of interest for the first two years it is 15% per year and for the third year it is 16%. So, first of all we have to determine the compound interest on the amount which was invested by the Prem who lends Rs. 100,000.
Now, we have to determine the amount if the rate of interest for the first two years it is 15% per year with the help of the formula which is as mentioned below:

Formula used:
$\Rightarrow A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}...............(1)$
Where, A is the compounded amount, P is the principal amount, R is the rate of interest and n is the time for which the principal amount is invested.
Now, we have to determine the amount of the rate of interest for the third year. It is 16% per year with the help of the formula (1) which is as mentioned above.
Now, after substituting all the values in the formula above, we can determine the sum of Rohit will get at the end of the third year.

Complete step-by-step answer:
Step 1: First of all we have to determine the compound interest on the amount which was invested by the Prem who lends Rs. 100,000. As mentioned in the solution hint.
Step 2: Now, to find the compounded amount which is invested at the rate of 15% for first two years and at the rate of 16% for the last year from the three years or we can say for the third year with the help of the formula (1) as mentioned in the solution hint. Hence, on substituting all the values in the formula (1),
$\Rightarrow 100000 \times {\left( {1 + \dfrac{{15}}{{100}}} \right)^2} \times {\left( {1 + \dfrac{{16}}{{100}}} \right)^1}$
Step 3: Now, to solve the arithmetic expression as in the solution step 2, we just have to determine the L.C.M and then we have to multiply each of the terms means we just have to simplify the obtained expression after finding the L.C.M.
$\Rightarrow 100000 \times {\left( {\dfrac{{115}}{{100}}} \right)^2} \times {\left( {\dfrac{{116}}{{100}}} \right)^1} \\\ \Rightarrow 100000 \times {\left( {\dfrac{{23}}{{20}}} \right)^2} \times {\left( {\dfrac{{29}}{{25}}} \right)^1} \\\$
Now, we have to find the square of the fraction as given in the expression obtained just above, hence,
$\Rightarrow 100000 \times \left( {\dfrac{{529}}{{400}}} \right) \times \left( {\dfrac{{29}}{{25}}} \right)$
Now, on multiplying and dividing all the terms of the expression just obtained above,
$\Rightarrow 100000 \times \dfrac{{529 \times 29}}{{10000}} \\\ \Rightarrow 10 \times 15341 \\\ \Rightarrow Rs.153410 \\\$
Final solution: Hence, with the help of the formula (1) as mentioned in the solution hint we have determined that the sum of Rohit will get at the end of the third year is $Rs.153410$.

Therefore, option (B) is correct.

Note:
To determine the required amount it is necessary that we have to determine the compound interest which is 15% for first two years and 16% for next one year or the third year.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.