1. **Problem statement:** Esmeralda wants to save enough money to buy a summer house priced at 990000 after 6.5 years by making equal quarterly deposits into a bank account with an interest rate of 2.5% per quarter. 2. **Formula used:** The future value of an ordinary annuity formula applies here: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where $FV$ is the future value (990000), $P$ is the quarterly payment, $r$ is the quarterly interest rate (2.5% = 0.025), and $n$ is the total number of quarters. 3. **Calculate $n$:** Since 6.5 years with 4 quarters per year: $$n = 6.5 \times 4 = 26$$ 4. **Rearrange formula to solve for $P$:** $$P = \frac{FV \times r}{(1 + r)^n - 1}$$ 5. **Substitute values:** $$P = \frac{990000 \times 0.025}{(1 + 0.025)^{26} - 1}$$ 6. **Calculate $(1 + 0.025)^{26}$:** $$1.025^{26} \approx 1.931677$$ 7. **Calculate denominator:** $$(1.931677 - 1) = 0.931677$$ 8. **Calculate numerator:** $$990000 \times 0.025 = 24750$$ 9. **Calculate $P$:** $$P = \frac{24750}{0.931677} \approx 26556.68$$ **Answer:** Esmeralda must deposit approximately 26556.68 every quarter to have 990000 after 6.5 years. --- **Sheet layout suggestion:** - Column A (Termin): 1, 2, ..., 26 - Column B (Rente): 0.025 (constant quarterly rate) - Column C (Indbetaling): 26556.68 (constant quarterly payment) - Column D (Saldo): Calculated using formula $$D_2 = C_2$$ $$D_{k} = D_{k-1} \times (1 + B_k) + C_k$$ for $k=3$ to 27 (rows correspond to quarters) This will show the growth of the savings each quarter until it reaches the target amount.