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.

(i) The amount credited against her name at the end of the second year.

(ii) The interest for the third year.

(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