Subjects finance

Nominal Interest 45B195

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1. **State the problem:** We need to find the nominal interest rate $i$ given the inflation rate $\pi = 4.57\% = 0.0457$ and the real interest rate $r = 3.28\% = 0.0328$. 2. **Formula used:** The Fisher equation relates nominal interest rate $i$, real interest rate $r$, and inflation rate $\pi$ as: $$1 + i = (1 + r)(1 + \pi)$$ This formula accounts for the effect of inflation on the real return of an investment. 3. **Calculate nominal interest rate:** Substitute the values: $$1 + i = (1 + 0.0328)(1 + 0.0457)$$ $$1 + i = 1.0328 \times 1.0457$$ $$1 + i = 1.08094996$$ 4. **Solve for $i$:** $$i = 1.08094996 - 1$$ $$i = 0.08094996$$ 5. **Convert to percentage:** $$i = 0.08094996 \times 100 = 8.094996\%$$ 6. **Round to two decimal places:** $$i \approx 8.09\%$$ **Final answer:** The nominal interest rate needed is **8.09\%**.