Question 1: Find the amount and the compound interest on Rs. \displaystyle 5000 for \displaystyle 2 years at \displaystyle 8\% per annum, compounded annually.

Answer:

\displaystyle \text{ Principal for the first year  } = 5000 \text{ Rs. }

\displaystyle \text{ Interest for the first year   } = \Big( \frac{8}{100} \Big) \times{}5000=400 \text{ Rs. }

\displaystyle \text{ Principal for the second year    } = 5400 \text{ Rs. }

\displaystyle \text{ Amount at the end of second year   } = (1+ \frac{8}{100} ) \times 5400 =5832 \text{ Rs. }

\displaystyle \text{Interest for the second year  } = \frac{8}{100} \time 5400 = 432 \text{ Rs. }

\displaystyle \text{Compound interest   } = 400+432=832 \text{ Rs. }

 \displaystyle \\

Question 2: Find the amount and the compound interest on Rs. \displaystyle 8000 for \displaystyle 2 years at \displaystyle 6\% per annum, compounded annually.

Answer:

\displaystyle \text{ Principal for the first year  } = 8000 \text{ Rs. }

\displaystyle \text{ Interest for the first year   } = \frac{6}{100} \times 8000 =480 \text{ Rs. }

\displaystyle \text{Principal for second year    }  = 8000+480=8480 \text{ Rs. }

\displaystyle \text{Interest for second year    } = \frac{6}{100} \times 8480=508.80 \text{ Rs. }

\displaystyle \text{Principal at the end of second year    } = 8480+508.80=8988.80 \text{ Rs. }

\displaystyle \text{Total compound interest    } = 480+508.80=988.80 \text{ Rs. }

 \displaystyle \\

Question 3: Find the amount and the compound interest on Rs. \displaystyle 2500 for \displaystyle 2 years, compounded annually, the rate of interest being \displaystyle 6\% during the first year and \displaystyle 8\% during second year.

Answer:

\displaystyle \text{ Principal for the first year  } = 2500 \text{ Rs. }

\displaystyle \text{Interest earned by end of first year    } = \frac{6}{100} \times 2500 = 150 \text{ Rs. }

\displaystyle \text{ Principal for the second year    } = 2500+150=2650 \text{ Rs. }

\displaystyle \text{Interest earned for second year    } = \frac{8}{100} \times 2650=212 \text{ Rs. }

\displaystyle \text{Total interest    } = 150+212=362 \text{ Rs. }

\displaystyle \text{Amount at the end of the second year    } = 2650+212=2862 \text{ Rs. }

 \displaystyle \\

Question 4: Find the amount and the compound interest on Rs. \displaystyle 2500 for \displaystyle 3 years at \displaystyle 6\% per annum, compounded annually.

Answer:

\displaystyle \text{ Principal for the first year  } = 25000 \text{ Rs. }

\displaystyle \text{Interest for first year    } = \frac{6}{100} \times 25000 =1500 \text{ Rs. }

\displaystyle \text{Principal for 2nd year    } = Rs.25000+1500=26500 \text{ Rs. }

\displaystyle \text{Interest for 2nd year    } = \frac{6}{100} \times 26500=1590 \text{ Rs. }

\displaystyle \text{Principal for 3rd year    } = 26500+1590=28090 \text{ Rs. }

\displaystyle \text{Interest for 3rd year    } = \frac{6}{100} \times 28090=1685.40 \text{ Rs. }

\displaystyle \text{Amount at the end of the 3rd year    } =28090+1685.4 =29775.4 \text{ Rs. }

 \displaystyle \\

Question 5: Find the amount and the compound interest on Rs. \displaystyle 10000 for \displaystyle 3 years at \displaystyle 10 \% per annum, compounded annually.

Answer:

\displaystyle \text{Principal for the 1st year    } = 10000 \text{ Rs. }

\displaystyle \text{Interest for 1st year    } = \frac{10}{100} \times 10000=1000 \text{ Rs. }

\displaystyle \text{Principal for 2nd year    } = 10000+100=11000 \text{ Rs. }

\displaystyle \text{Interest for 2nd year    } = \frac{10}{100} \times 11000=1100 \text{ Rs. }

\displaystyle \text{Principal for 3rd year    } = 11000+1100=12100 \text{ Rs. }

\displaystyle \text{Interest for 3rd year    } = \frac{10}{100} \times 121000=1210 \text{ Rs. }

\displaystyle \text{Amount at the end of the 3rd year    } = 12100+1210=13310 \text{ Rs. }

\displaystyle \text{Total compounded interest    } = 1000+1100+1210=3210 Rs.

 \displaystyle \\

Question 6: ‘A’ took a loan of Rs. \displaystyle 25000 from corporate bank at \displaystyle 12\% per annum, compounded annually. How much amount he will have to pay at the end of \displaystyle 3 years?

Answer:

\displaystyle \text{Principal for the 1st year    } = 25000 \text{ Rs. }

\displaystyle \text{Interest for the 1st year    } = \frac{12}{100} \times 25000=3000 \text{ Rs. }

\displaystyle \text{Principal for 2nd year    } = 28000 \text{ Rs. }

\displaystyle \text{Interest on 2nd the year    } = \frac{12}{100} \times 28000=3360 \text{ Rs. }

\displaystyle \text{Principal for the 3rd year    } = 31600 \text{ Rs. }

\displaystyle \text{Interest for the 3rd year    } = \frac{12}{100} \times 31360=3763.2 \text{ Rs. }

\displaystyle \text{Amount at the end of 3rd year    } = 35123.20 \text{ Rs. }

\displaystyle \text{ Total compounded interest  } = 10152 \text{ Rs. }

 \displaystyle \\

Question 7: ‘A’ deposited Rs. \displaystyle 15625 in a bank at \displaystyle 8\% per annum, compounded annually. How much amount will he get after \displaystyle 3 years?

Answer:

\displaystyle \text{Principal for 1st year    } = 15625 \text{ Rs. }

\displaystyle \text{Interest for 1st year    } = \frac{8}{100} \times 15625=1250 \text{ Rs. }

\displaystyle \text{Principal for 2nd year    } = 16875 \text{ Rs. }

\displaystyle \text{Interest for 2nd year    } = \frac{8}{100} \times 16875=1350 \text{ Rs. }

\displaystyle \text{Principal for the 3rd year    } = 18225 \text{ Rs. }

\displaystyle \text{ Interest for the 3rd year  } = \frac{8}{100} \times 18225=1458 \text{ Rs. }

\displaystyle \text{Amount at the end of the 3rd year    } = 19683 \text{ Rs. }

 \displaystyle \\

Question 8: A person lent out Rs. \displaystyle 16000 on simple interest and the same sum on compound interest for \displaystyle 2 years at \displaystyle 12.5\% per annum. Find the ratio of the amounts received by him as interest after \displaystyle 2 years.

Answer:

Simple Interest

Principal for the 1st year \displaystyle = 16000 \text{ Rs. }

Interest for the 1st year \displaystyle = \frac{12.5}{100} \times 16000=2000 \text{ Rs. }

Interest for 2nd year \displaystyle = 2000 \text{ Rs. }

Total interest \displaystyle = 4000 \text{ Rs. }

Compound Interest

Principal for 1st year \displaystyle = 16000 \text{ Rs. }

Interest at the end of the 1st year \displaystyle = \frac{12.5}{100} \times 16000=2000 \text{ Rs. }

Principal for 2nd year \displaystyle = 18000 \text{ Rs. }

Interest at the end of the 2nd year \displaystyle = \frac{12.5}{100} \times 18000=2250 \text{ Rs. }

Total compound interest \displaystyle =2000+2250=4250 \text{ Rs. }

Ratio of the interest \displaystyle = 4000 \colon 4250 \ or \ 16 \colon 17

 \displaystyle \\

\displaystyle \text{ Note: We could also solve by using the formula  } A=P \Big\{ \Big( 1+ \frac{r}{100} \Big) \Big\}^n

\displaystyle \text{Answer 1:    } A=5000 \Big\{ \Big( 1+ \frac{8}{100} \Big) \Big\}^2 = 5832 \text{ Rs. }

\displaystyle \text{Answer 2:    } A=8000 \Big\{ \Big( 1+ \frac{6}{100} \Big) \Big\}^2 = 8988.80 \text{ Rs. }

\displaystyle \text{Answer 3:    } A=25000 \Big\{ \Big( 1+ \frac{6}{100} \Big) \Big\}^2 =29775.4 \text{ Rs. }

\displaystyle \text{Answer 4:    } A=10000 \Big\{ \Big( 1+ \frac{10}{100} \Big) \Big\}^2 =13310 \text{ Rs. }

\displaystyle \text{Answer 5:    } A=25000 \Big\{ \Big( 1+ \frac{12}{100} \Big) \Big\}^2 =35123.2 \text{ Rs. }

\displaystyle \text{Answer 6:    } A=15625 \Big\{ \Big( 1+ \frac{8}{100} \Big) \Big\}^2 =19683 \text{ Rs. }

\displaystyle \text{Answer 7:    } A=16000 \Big\{ \Big( 1+ \frac{12.5}{100} \Big) \Big\}^2 = 20250 \text{ Rs. }