1. **State the problem:** Mrs. Ninyel wants to have 2,000,000 in 4 years by depositing a lump sum today in an account with 8% interest compounded quarterly. 2. **Formula used:** The compound interest formula for future value is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after time $t$ - $P$ is the principal (initial deposit) - $r$ is the annual interest rate (decimal) - $n$ is the number of compounding periods per year - $t$ is the time in years 3. **Given values:** - $A = 2,000,000$ - $r = 0.08$ - $n = 4$ (quarterly compounding) - $t = 4$ 4. **Rearrange formula to find $P$:** $$P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}$$ 5. **Substitute values:** $$P = \frac{2,000,000}{\left(1 + \frac{0.08}{4}\right)^{4 \times 4}} = \frac{2,000,000}{\left(1 + 0.02\right)^{16}} = \frac{2,000,000}{1.02^{16}}$$ 6. **Calculate $1.02^{16}$:** $$1.02^{16} \approx 1.372786$$ 7. **Calculate $P$:** $$P = \frac{2,000,000}{1.372786}$$ 8. **Show cancellation:** $$P = \frac{2,000,000}{\cancel{1.372786}} \approx 1,456,349.42$$ 9. **Answer:** Mrs. Ninyel must deposit approximately **1,456,349.42** today to have 2,000,000 in 4 years at 8% compounded quarterly.