A sum was lent at 20% p.a compound interest, the interest being compounded annually. Rs. 1200 was paid back after 1 year. after another year rs. 1440 was repaid to clear the loan. find the sum lent? 

consider 2nd year. he has paid 1440 and clear the debt.

so the let amount remaining after 1st year (giving 1200) be 'P'

p(1+(20/100))^1=1440

p=1200

so the total amount after 1st year =1200+1200=2400

p(1+(20/100))^1=2400

p=2000

1200/1.2 + 1440/1.2*1.2 = 2000rs.

P= [x1/{1+(R/100)}^1]+[x2/{1+(R/100)}^2]+........+[xn/{1+(R/100)}^n]
p= 1200/(1+20/100)+1440/(1+20/100)^2
=(36000+36000)/36
=2000