Q.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 = $Rs.\ 5000$

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.

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.

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.

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.

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?

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?

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.

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