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7.Maria invested ₹ 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find
(i) The amount credited against her name at the end of the second year.

(ii) The interest for the third year.


Answer :

(i) Given: P = ₹ 8,000, R = 5% p.a. and n = 2 years

Amount=\(P(1+\frac{R}{100})^n\)

=\(8,000(1+\frac{5}{100})^2\)

=\(8,000(\frac{21}{20})^2\)

=\(8,000\times(\frac{21}{20}\times \frac{21}{20})\)

=\(20\times 441\)

=\(₹ \; 8,820\)

Thus, the amount credited at the end of 2 years=₹ 8,820

(ii) Interest for the third year=Amount after 3 years - Amount after 2 years

=\(P(1+\frac{R}{100})^n\) - ₹ 8,820

=\(8,000(1+\frac{5}{100})^3\) - ₹ 8,820

=\(8,000(\frac{21}{20})^3\) - ₹ 8,820

=\(8,000\times(\frac{21}{20}\times \frac{21}{20}\times \frac{21}{20})\) - ₹ 8,820

= ₹ 9,261 - ₹ 8,820

= ₹ 441

Hence we got, interest for the third year = ₹ 441