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

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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.

Answer:

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?

Answer:

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?

Answer:

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.

Answer:

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.