Question

*In how many years Rs. 6000 will amount to Rs. 7986 at 10% rate at compound interest?*

1️⃣ 1 year
2️⃣ 2 years
3️⃣ 3 years
4️⃣ 4 years​

Answer 1

Answer:

interest of 1st year is 10% of 6000= 600

interest of 2nd year is 10% of 6600 = 660

interest of 3rd year is 10% of 7260= 726

after 3 year amount will be 6000+600+660+726= 7986

therefore option 3 is correct

Answer 2

Rs. 6000 will amount to Rs. 7986 at the 10% rate at compound interest in 3 years. (option 3)

• The formula of the amount is given by $Amount=Principal(1+\frac{r}{100})^n$.

• Substitute Amount equal to Rs. 7986, Principal equal to Rs. 6000, and the rate is equal to 10.

• $7986=6000(1+\frac{10}{100})^n\\\frac{7986}{6000}= (1+\frac{1}{10})^n\\\frac{1331}{1000}= (\frac{11}{10})^n$

• 1331 is the cube of 11 and 1000 is the cube of 10. So, replace 1331 by $11^3$ and 1000 by $10^3$.

        $\frac{11^3}{10^3}= (\frac{11}{10})^n\\(\frac{11}{10})^3= (\frac{11}{10})^n$

• Since the base at both sides is the same so power can be equated.

        $n=3$

• Thus, in 3 years Rs. 6000 will amount to Rs. 7986 at the 10% rate at compound interest.