(a) Principal (P) = Rs 10, 800

Rate (R) 12 1/2% = 25/2% ( annual )

Number of years (n) = 3

Amount, A = p( 1 + R/100 )^{n}

= Rs [10800 (1 + 25/200)^{3}]

= Rs [10800(225/200)^{3}]

= Rs ( 10800 x 225/200 x 225/200 x 225/200 )

= Rs 15377.34375

= Rs 15377.34 (approximately)

C.I. = A − P = Rs (15377.34 − 10800) = Rs 4,577.34

(b) Principal (P) = Rs 18,000

Rate (R) = 10% annual

Number of years (n) = 2 1/2 years

The amount for 2 years and 6 months can be calculated by first calculating the amount for 2 years using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 2 years. Firstly, the amount for 2 years has to be calculated.

A = Rs [18000( 1 + 1/10 )^{2}]

= Rs (18000 x 11/10 x 11/10)

= Rs 21780

By taking Rs 21780 as principal, the S.I. for the next 1/2 year will be calculated.

S.I = Rs (21780 x 1/2 x 10 / 100) = Rs 1089

∴ Interest for the first 2 years = Rs (21780 − 18000) = Rs 3780

And interest for the next 1/2 year = Rs 1089

∴ Total C.I. = Rs 3780 + Rs 1089 = Rs 4,869

A = P + C.I. = Rs 18000 + Rs 4869 = Rs 22,869

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