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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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?

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

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

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

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

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

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

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

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

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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?

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

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

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

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

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

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

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

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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.

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 $\displaystyle = 4000 \colon 4250 \ or \ 16 \colon 17$

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

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

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

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

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

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

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

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