1. **Stating the problem:** United Bank offers two interest rates for fixed deposits. We need to understand how to calculate the interest earned using these rates. 2. **Formula for simple interest:** $$I = P \times r \times t$$ where $I$ is the interest earned, $P$ is the principal amount, $r$ is the annual interest rate (in decimal), and $t$ is the time in years. 3. **Formula for compound interest:** $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where $A$ is the amount after interest, $P$ is the principal, $r$ is the annual interest rate (decimal), $n$ is the number of times interest is compounded per year, and $t$ is the time in years. 4. **Important rules:** - Convert percentage rates to decimals by dividing by 100. - For fixed deposits, interest is often compounded quarterly, half-yearly, or yearly. - The total interest earned is $I = A - P$. 5. **Example calculation:** Suppose $P=10000$, $r=5\% = 0.05$, $t=2$ years, compounded quarterly ($n=4$). Calculate $A$: $$A = 10000 \left(1 + \frac{0.05}{4}\right)^{4 \times 2} = 10000 \left(1 + 0.0125\right)^8 = 10000 \times 1.104486 = 11044.86$$ Interest earned: $$I = 11044.86 - 10000 = 1044.86$$ This means after 2 years, the fixed deposit grows to 11044.86 with an interest of 1044.86. 6. **Summary:** Use the compound interest formula for fixed deposits with the given rate and compounding frequency to find the final amount and interest earned.