1. **State the problem:** We need to find the compound amount and the interest earned on $78000 at an interest rate of 0.94% compounded quarterly for 7 years. 2. **Formula for compound interest:** $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the compound amount (final amount), - $P$ is the principal (initial amount), - $r$ is the annual interest rate (decimal), - $n$ is the number of compounding periods per year, - $t$ is the time in years. 3. **Identify values:** - $P = 78000$ - $r = 0.94\% = 0.0094$ - $n = 4$ (quarterly compounding) - $t = 7$ 4. **Calculate compound amount:** $$A = 78000 \left(1 + \frac{0.0094}{4}\right)^{4 \times 7} = 78000 \left(1 + 0.00235\right)^{28} = 78000 \times 1.00235^{28}$$ 5. Calculate $1.00235^{28}$: $$1.00235^{28} \approx 1.0673$$ 6. Multiply to find $A$: $$A = 78000 \times 1.0673 = 83219.40$$ 7. **Calculate interest earned:** $$\text{Interest} = A - P = 83219.40 - 78000 = 5219.40$$ **Final answers:** - Compound amount: $83219.40$ - Interest earned: $5219.40$