State T for true and $ \mathrm{F} $ for false.(i) Compound interest is calculated by using the formula, C.I. $ =P\left(1+\frac{r}{100}\right)^{n} $(ii) The simple interest and the compound interest on the same principal for same time period $ (>1 $ year) and at the same rate of interest are not equal.(iii) If a sum of ₹ 2000 becomes ₹ 2600 after three years, then rate of simple interest is $ 10 \% $ per annum. (iv) In case of compound interest, the principal remains constant throughout the time period.

(i) If the interest is compounded annually, the amount is given as:

C.I. \( =P\left(1+\frac{r}{100}\right)^{n} \)

The above statement is true. (T)
(ii)  The simple interest and the compound interest on the same principal for same time period \( (>1 \) year) and at the same rate of interest are not equal.

The above statement is true. (T)

(iii) $P=Rs.\ 2000, R=10 \%, T=3$ years.

Therefore,

$A=P+SI$

$=2000+\frac{2000\times10\times3}{100}$

$=2000+600$

$=2600$

Hence, if a sum of ₹ 2000 becomes ₹ 2600 after three years, then rate of simple interest is \( 10 \% \) per annum.

The above statement is true. (T)

(iv) In case of simple interest the principal remains the same for the whole period but in case of compound interest the principal changes every year. 

The above statement is false. (F)