Interest and Interest Rate Calculation

The principal is $\pounds 100$, and the annual interest rate is $6\%$. Multiply the principal by the interest rate: $\pounds 100\times 6\%=\pounds 6$. So, you will earn $\pounds 6$ in interest after 1 year.

The principal is $\pounds 60$, and the annual interest rate is $5\%$. Multiply the principal by the interest rate: $\pounds 60\times 5\%=\pounds 3$.

The yearly interest is $\pounds 400\times 2\%=\pounds 8$. Since 3 months is one-quarter of a year, the interest earned is $\pounds 8÷4=\pounds 2$.

The interest for one year is $\pounds 250\times 4\%=\pounds 10$. Add this to the principal: $\pounds 250+\pounds 10=\pounds 260$.

The interest earned is $\pounds 1030-\pounds 1000=\pounds 30$. Using $\text{Interest}=\text{Principal}\times \text{Rate}$, we get $30=1000\times \text{Rate}$. So, $\text{Rate}=\frac{30}{1000}=0.03$, which is $3\%$.

Since 6 months is half a year, double the interest to find the yearly interest: $\pounds 18\times 2=\pounds 36$. Using $\text{Interest}=\text{Principal}\times \text{Rate}$, we have $36=\text{Principal}\times 3\%$. So, $\text{Principal}=\frac{36}{0.03}=\pounds 1200$.