1. **Problem:** Find the nominal interest rate compounded quarterly for 2.75 years that will accumulate P 120,000 to an interest of P 25,000. 2. **Formula:** Compound interest formula: $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ where $A$ is the amount, $P$ is the principal, $r$ is the nominal annual interest rate, $n$ is the number of compounding periods per year, and $t$ is time in years. 3. **Given:** $P=120000$, interest $I=25000$, so $A = P + I = 145000$, $t=2.75$ years, $n=4$ (quarterly). 4. **Calculate $r$:** $$145000 = 120000\left(1 + \frac{r}{4}\right)^{4 \times 2.75}$$ $$\left(1 + \frac{r}{4}\right)^{11} = \frac{145000}{120000} = 1.2083333$$ 5. Take the 11th root: $$1 + \frac{r}{4} = (1.2083333)^{\frac{1}{11}}$$ Calculate: $$ (1.2083333)^{\frac{1}{11}} \approx 1.0175$$ 6. Solve for $r$: $$\frac{r}{4} = 1.0175 - 1 = 0.0175$$ $$r = 0.0175 \times 4 = 0.07 = 7\%$$ **Answer:** The nominal rate compounded quarterly is **7%**. --- **Note:** Due to the GUEST RULE, only the first question is solved here.