1. **State the problem:** Ramani deposited an amount $P$ for two years at an annual compound interest rate of 10%. The interest earned in the second year is 660 and the total amount after two years is 7260. We need to find the principal amount $P$. 2. **Formula for compound interest:** The amount after $n$ years with interest rate $r$ compounded annually is given by: $$ A = P(1 + r)^n $$ where $A$ is the amount, $P$ is the principal, $r$ is the rate in decimal, and $n$ is the number of years. 3. **Calculate the amount after the first year:** $$ A_1 = P(1 + 0.10) = 1.1P $$ 4. **Calculate the amount after the second year:** $$ A_2 = A_1(1 + 0.10) = 1.1 imes 1.1P = 1.21P $$ 5. **Given total amount after two years:** $$ A_2 = 7260 $$ So, $$ 1.21P = 7260 $$ 6. **Calculate principal $P$ from total amount:** $$ P = \frac{7260}{1.21} $$ $$ P = \frac{7260}{\cancel{1.21}} \times \cancel{\frac{1}{1.21}} = 6000 $$ 7. **Calculate interest for the second year:** Interest for second year = Amount at end of second year - Amount at end of first year $$ = 1.21P - 1.1P = 0.11P $$ Given this interest is 660, $$ 0.11P = 660 $$ 8. **Calculate principal $P$ from second year interest:** $$ P = \frac{660}{0.11} = 6000 $$ 9. **Conclusion:** Both methods confirm the principal amount deposited is **6000**.