Question

A man borrowed a sum of money and agrees to pay off by paying Rs. 6000 at the end of the first year and Rs. 7812 at the end of the second year. If the rate of compound interest is 5% per annum, then the sum borrowed is​

Answer 1

Answer:

12800

Step-by-step explanation:

6000/1.05+7812/1.05^2

=12800

Answer 2

$\\ \huge{ \underline{ \underline{ \purple{ \sf{ \pmb{Question}}}}}}$

A man borrowed a sum of money and agrees to pay off by paying Rs. 6000 at the end of the first year and Rs. 7812 at the end of the second year. If the rate of compound interest is 5% per annum, then what is the sum borrowed?

$\\ \huge{ \underline{ \underline{ \purple{ \sf{ \pmb{Required \: Answer}}}}}}$

$\\ \large{ \underline{ \underline{ \sf{ \pmb{Given}}}}}$

• In first year, agreed to pay Rs.6000
• In second year,agreed to pay Rs.7812
• Rate of the compound interest 5%

$\\ \large{ \underline{ \underline{ \sf{ \pmb{To \: Find}}}}}$

• The sum borrowed by the man.

$\\ \large{ \underline{ \underline{ \sf{ \pmb{Solution}}}}}$

We know that:-

• $\\ \underline{ \boxed{ \bold{ \tt{A= P(1 + \dfrac{r}{100}) {}^{n}}}}}$

Where,

• A = Amount
• P = Principal amount
• r = Rate of interest
• n = Number of time

For the payment of Rs.6000 at the end of the first year :-

• A = Rs.6000
• n = 1 year and
• r = 5%

To find P :-

$\\ \bold{6000 = P_{1 }(1 + \dfrac{5}{100}) {}^{1}}$

$\\ \sf{ \implies{6000 = P_{1 }(1 + 0.05) {}^{1} }}$

$\\ \sf{ \implies{6000 = P_{1 } \times 1.05}}$

$\\ \sf{ \implies{P_{1 }= \dfrac{6000}{1.05} }}$

$\\ \sf{ \therefore{ \bold{P_{1 } = Rs.\dfrac{40000}{7}}}}$

Again,

For the payment of Rs.7812 at the end of the second year :

• A = Rs.7812
• n = 2 years and
• r = 5%

Therefore,

$\\ \sf{ \implies{ \bold{A = P(1 + \dfrac{r}{100}) {}^{n}}}}$

$\\ \sf{ \implies{7812 = P_{2} (1 + \frac{5}{100}) {}^{2}} }$

$\\ \sf{ \implies{7812 = P_{2} (1 + 0.05) {}^{2} }}$

$\\ \sf{ \implies{7812= P_{2} \times 1.05 {}^{2} }}$

$\\ \sf{ \implies{7812 = P_{2} \times 1.1025}}$

$\\ \sf{ \implies{P_{2} = \dfrac{7812}{1.1025} }}$

$\\ \sf{ \therefore{ \bold{P_{2} = Rs.\dfrac{49600}{7}}}}$

Now,

$\\ \sf{Sum \: borrowed :- }$

$\\ \sf{= P_{1 }+ P_{2} =Rs.( \dfrac{40000}{7}+\dfrac{49600}{7} ) = \red{Rs.12800}}$

Hence, the man borrowed Rs. 12800