1. Calculate the amount and the compound interest for each of the following: (a) ₹ 7,500 at 12% p.a. in 3 years. (b) ₹ 13,500 at 10% p.a. in 2 years.
1. Calculate the amount and the compound interest for each of the following: (a) ₹ 7,500 at 12% p.a. in 3 years. (b) ₹ 13,500 at 10% p.a. in 2 years.

(a) 7,500 at 12% p.a. in 3 years.

Solution:-

Principal = P

Rate = R

Time = T   

Given :

Principal, P = ₹ 7,500, Rate, r = 12% p.a., Time, t = 3 years

For the first year, t = 1 year

S.I. = (P × r × t)/100

= (7,500\times 12\times 1)/100.

= ₹ 900

A = P + S.I.

= 7,500 + 900

= ₹ 8,400

New principal is ₹ 8,400.

For the second year, t = 1 year, p = ₹ 8,400

S.I. = (P × r × t)/100

= (8,400\times 12\times 1)/100

= ₹ 1,008

A = P + S.I.

= 8,400 + 1,008

= ₹ 9,408

New principal is ₹ 9,408.

For the Third year, t = 1 year, p = ₹ 9,408

S.I. = (P × r × t)/100

= (9,408\times 12\times 1)/100

= ₹ 1,128.96

A = P + S.I.

= 9,408 + 1,128.96

= ₹ 10,536.96

C.I. = Interest in first year + interest in second year + interest in third year

= ₹ (900 + 1,008 + 1,128.96)

= ₹ 3,036.96

Solution:-

P = ₹ 13,500, r = 10% p.a., t = 2 years

For the first year, t = 1 year

S.I. = (P × r × t)/100

= (13,500\times 10\times 1)/100

= ₹ 1,350

A = P + S.I.

= 13,500 + 1,350

= ₹ 14,850

New principal is ₹ 14,850.

For the second year, t = 1 year, p = ₹ 14,850

S.I. = (P × r × t)/100

= = (14,850\times 10\times 1)/100

= ₹ 1,485

A = P + S.I.

= 14,850 + 1,485

= ₹ 16,335

C.I. = Interest in first year + interest in second year

= ₹ (1,350 + 1,485)

= ₹ 2,835