Question

12. A man borrows Rs. 21000 at 10% compound||
interst, How much he has to pay annually at the
end of cash year, to settle his loan in two years?
A) Rs. 12000
B) Rs. 12100
C) Rs. 12200
D) Rs. 12300​

Answer 1

The answer of this ques is A

Answer 2

Man has to pay Rs. 12100 annually.

Step-by-step explanation:

formula for compound interest         $A=P[1+\dfrac{r}{100}]^{n}$

Let he pay Rs. $x$ yearly to settle his loan.

• now, the principal for the first year is 21000 and rate is 10 % compound yearly.
• so, amount after first year ($A_1$) = $21000[1+\dfrac{10}{100}]^{1}$

                                            ($A_1$) = 23100  Rs.

he pays Rs. $x$ after first year.

so remaining amount after first year = ($A_1$) -  $x$

Now,  [ ($A_1$) -  $x$ ]is the principal for the second year compound interest,

so the amount for second year ($A_2$) = $[A_1 -x][1+\dfrac{10}{100}]^{1}$ = (23100 -  $x$) × $\dfrac{11}{10}$

      but amount of second year  ($A_2$) = installment  $x$

                                     ∴     (23100 -  $x$) × $\dfrac{11}{10}$   =   $x$

                                ∴ 21  $x$  = 11 × 23100

                                        $x$ = 12100

so each year installment is Rs. 12100.