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# 1. Calculate the amount and compound interest on (a)₹ 10,800 for 3 years at $$12\frac { 1 }{ 2 }$$ % per annum compounded annually. (b)₹ 18,000 for $$2\frac { 1 }{ 2 }$$ years at 10% per annum compounded annually. (c)₹ 62,500 for $$1\frac { 1 }{ 2 }$$ years at 8% per annum compounded half yearly. (d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify). (e)₹ 10,000 for 1 year at 8% per annum compounded half yearly.

(a) Given, P=₹ 10,800,n=3 years.
We have, R=$$12\frac{1}2$$% = $$\frac{25}2$$%p.a.

So, we know that $$Amount=P(1+\frac{R}{100})^n$$

$$=10,800(1+\frac{25}{100})^3$$

$$=10,800(\frac{9}{8})^3$$

$$=10,800\times(\frac{9}{8})\times(\frac{9}{8})\times(\frac{9}{8})$$

$$=\frac{4,92,075}{32}=₹ \; 15,377.34$$
Thus, we have Compound interest=A - P

=₹ 15,377.34-₹ 10,800 = ₹ 4,577.35

Hence we have, amount = ₹ 15,377.34 and CI = ₹ 4,577.34

(b)We have: P = ₹ 18,000, n = $$2\frac { 1 }{ 2 }$$ years and R = 10% p.a.
The amount for $$2\frac { 1 }{ 2 }$$ years, can be calculated by first calculating the amount to 2 years using CI formula and then calculating the simple interest by using SI formula.

The amount for 2 years:

Amount = $$18000(1+\frac{10}{100})^2$$

= $$18000\times(\frac{110}{100})^2$$

= $$18000\times(\frac{11}{10})\times(\frac{11}{10})=₹ \; 21,780$$

∴ Interest after 2 years = Amount - P

=21,780-18,000=₹ 3,780

So, now taking principal amount as ₹ 21,780, the SI for the next $$\frac{1}2$$years will be as:

SI=$$\frac{P\times R\times n}{100}$$

=$$\frac{21,780\times10\times1}{100\times2}$$

=$$₹\; 1,089$$

Therefore,Total CI = ₹ 3780 +₹ 1,089= ₹ 4,869

Amount = P + I = ₹ 21,780 + ₹ 1,089 =₹ 22,869

Hence, the amount = ₹ 22,869 and CI = ₹ 4,869
(c)Given, P=₹ 62,500,n=$$1\frac{1}2=\frac{3}2$$ years per annum compounded half yearly i.e., $$\frac{3}2\times 2$$ years=3 half years.
We have, R=$$8$$%=$$\frac{8}2$$% = $$4$$%half yearly

So, we know that $$Amount=P(1+\frac{R}{100})^n$$

$$=62,500(1+\frac{4}{100})^3$$

$$=62,500(\frac{26}{25})^3$$

$$=62,500\times(\frac{26}{25})\times(\frac{26}{25})\times(\frac{26}{25})$$

$$=4 \times 26\times 26\times 26=₹ \; 70,304$$
Thus, we have Compound interest=A - P

=₹ 70,304-₹ 62,500 = ₹ 7,804

Hence we have, amount = ₹ 70,304 and CI = ₹ 7804
(d)Given, P=₹ 8,000,n=1 years and R = 9% per annum compounded half yearly
Since, the interest is compounded half yearly n =$$1 \times 2 = 2$$ half years.So, R=$$\frac{9}2$$% per half years.

So, we know that $$Amount=P(1+\frac{R}{100})^n$$

$$=8,000(1+\frac{9}{2\times100})^2$$

$$=8,000(\frac{209}{200})^2$$

$$=8,000\times(\frac{209}{200})\times(\frac{209}{200})$$

$$=₹ \;(\frac{8,7362}{10})$$

$$=₹ \; 8,736.20$$

Thus, we have Compound interest=A - P

=₹ 8,736.20-₹ 8,000 = ₹ 736.20

Hence we have, amount = ₹ 8736.20 and CI = ₹ 736.20
(e)Given, P=₹ 10,000,n=1 years and R = 8% per annum compounded half yearly
Since, the interest is compounded half yearly n =$$1 \times 2 = 2$$ half years.So, R=$$\frac{8}2=4$$% per half years.

So, we know that $$Amount=P(1+\frac{R}{100})^n$$

$$=10,000(1+\frac{4}{100})^2$$

$$=10,000(\frac{26}{25})^2$$

$$=10,000\times(\frac{26}{25})\times(\frac{26}{25})$$

$$=16\times 26\times 26$$

$$=₹ \; 10,816$$

Thus, we have Compound interest=A - P

=₹ 10,816 -₹ 10,000 = ₹ 816

Hence we have, amount = ₹ 10,816 and CI = ₹ 816