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

Principal for the first year $= 5000$ Rs.

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

Principal for the second year $= 5400$ Rs.

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

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

Compound interest $= 400+432=832$ Rs.

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

Principal for the first year $= 8000$ Rs.

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

Principal for second year $= 8000+480=8480$ Rs.

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

Principal at the end of second year $= 8480+508.80=8988.80$ Rs.

Total compound interest $= 480+508.80=988.80$ Rs.

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

Principal for the first year $= 2500$ Rs.

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

Principal for the second year $= 2500+150=2650$ Rs.

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

Total interest $= 150+212=362$ Rs.

Amount at the end of the second year $= 2650+212=2862$ Rs.

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

Principal for the first year $= 25000$ Rs.

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

Principal for 2nd year $= Rs.25000+1500=26500$ Rs.

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

Principal for 3rd year $= 26500+1590=28090$ Rs.

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

Amount at the end of the 3rd year $=28090+1685.4 =29775.4$ Rs.

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

Principal for the 1st year $= 10000$ Rs.

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

Principal for 2nd year $= 10000+100=11000$ Rs.

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

Principal for 3rd year $= 11000+1100=12100$ Rs.

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

Amount at the end of the 3rd year $= 12100+1210=13310$ Rs.

Total compounded interest $= 1000+1100+1210=3210 Rs.$

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

Principal for the 1st year $= 25000$ Rs.

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

Principal for 2nd year $= 28000$ Rs.

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

Principal for the 3rd year $= 31600$ Rs.

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

Amount at the end of 3rd year $= 35123.20$ Rs.

Total compounded interest $= 10152$ Rs.

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

Principal for 1st year $= 15625$ Rs.

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

Principal for 2nd year $= 16875$ Rs.

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

Principal for the 3rd year $= 18225$ Rs.

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

Amount at the end of the 3rd year $= 19683$ Rs.

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

Simple Interest

Principal for the 1st year $= 16000$ Rs.

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

Interest for 2nd year $= 2000$ Rs.

Total interest $= 4000$ Rs.

Compound Interest

Principal for 1st year $= 16000$ Rs.

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

Principal for 2nd year $= 18000$ Rs.

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

Total compound interest $=2000+2250=4250$ Rs.

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

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

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

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

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

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

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

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

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