Q.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 = Rs.\ 5000

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

Principal for the second year =Rs.5400

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

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

Compound interest = 400+432=832 Rs.

 

Q.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 = Rs.8000    

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.    

 

Q.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 = Rs.2500    

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.    

 

Q.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 = Rs.25000    

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    

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

 

Q.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 = Rs.10000    

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.    

 

Q.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 = Rs.25000    

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

Principal for 2nd year = Rs.28000    

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 = Rs.10152    

 

Q.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 = Rs.15625        

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

Principal for 2nd year = Rs.16875    

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

Principal for the 3rd year = Rs.18225    

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

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

 

Q.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 = Rs.16000    

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

Interest for 2nd year = Rs.2000    

Total interest = Rs.4000    

Compound Interest

Principal for 1st year = Rs.16000    

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

Principal for 2nd year = Rs.18000    

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    

 

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

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

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

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

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

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

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

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

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