A. Write true of false:
a. If Principal `=Rs.p`, rate of compound interest per annum `=r%` and time `=n` years, then the amount after 2 years is `Rs. p(1+r/100)^(2)`
b. If principal `=Rs. p` and rate of compound interest per annum for first, 2nd and 3rd year be `r_(1)%, r_(2)%` and `r_(3)%` respectively, then total amount for 3 years.
`=Rs. p(1+(r_(1))/100)^(3)+Rs. p(1+(r_(2))/100)^(3)+Rs. p(1+(r_(3))/100)^(3)`

Explanation

a. True since simple interest after 1 year `=Rs. (pxxrxx1)/100=Rs. (pr)/100`
`:.` amount after 1 year `=Rs. P+Rs. (pr)/100=Rs. P(1+r/100)`
Again simple interest of new principal `Rs. P(1+r/100)`
for 2nd year `Rs. (p(1+r/100)xxrxx1)/100=Rs. (pr(1+r/100))/100`
`:.` Amount after 2 year `=Rs. p(1+r/100)+Rs. (pr(1+r/100))/100`
`=Rs. p(1+r/100)(1+r/100)=Rs. p(1+r/100)^(2)`
Hence amount after 2 years `=Rs. p(1+r/100)^(2)`
False: Since the total amount for 3 years
`=Rs. p(1+(r_(1))/100)(1+(r_(2))/100)(1+(r_(3))/100)`