1. **State the problem:** Kiara invests 125 every month for 1 year (12 months) in two different annuities. - Annuity A: 2% annual interest compounded monthly + 25 bonus (no interest on bonus) - Annuity B: 3.9% annual interest compounded monthly We want to find which annuity yields more money after 1 year and by how much. 2. **Calculate future value of Annuity A:** - Monthly interest rate $i_A = \frac{2\%}{12} = 0.0016667$ - Number of payments $n = 12$ - Monthly payment $P = 125$ - Future value of ordinary annuity formula: $$FV = P \times \frac{(1+i)^n - 1}{i}$$ Calculate: $$FV_A = 125 \times \frac{(1+0.0016667)^{12} - 1}{0.0016667}$$ Calculate $(1+0.0016667)^{12}$: $$ (1.0016667)^{12} \approx 1.0201 $$ So: $$FV_A = 125 \times \frac{1.0201 - 1}{0.0016667} = 125 \times \frac{0.0201}{0.0016667} = 125 \times 12.06 = 1507.5$$ Add the $25$ bonus (no interest): $$FV_A^{total} = 1507.5 + 25 = 1532.5$$ 3. **Calculate future value of Annuity B:** - Monthly interest rate $i_B = \frac{3.9\%}{12} = 0.00325$ - Number of payments $n = 12$ - Monthly payment $P = 125$ Calculate: $$FV_B = 125 \times \frac{(1+0.00325)^{12} - 1}{0.00325}$$ Calculate $(1+0.00325)^{12}$: $$ (1.00325)^{12} \approx 1.0400 $$ So: $$FV_B = 125 \times \frac{1.0400 - 1}{0.00325} = 125 \times \frac{0.0400}{0.00325} = 125 \times 12.31 = 1538.75$$ 4. **Compare the two annuities:** Difference: $$1538.75 - 1532.5 = 6.25$$ 5. **Conclusion:** Annuity B is a better choice; it earns 6.25 more after 1 year.