1. **State the problem:** We need to find the size of the monthly payments that are equivalent to an immediate payment of 21100, given an interest rate of 4.6% compounded monthly over 12 years. 2. **Formula used:** The present value of an annuity formula is used to find the monthly payment $P$: $$PV = P \times \frac{1 - (1 + i)^{-n}}{i}$$ where: - $PV$ is the present value (21100), - $i$ is the monthly interest rate, - $n$ is the total number of payments. 3. **Calculate parameters:** - Annual interest rate = 4.6% = 0.046 - Monthly interest rate $i = \frac{0.046}{12} = 0.003833$ (rounded to six decimals) - Number of payments $n = 12 \times 12 = 144$ 4. **Rearrange formula to solve for $P$:** $$P = PV \times \frac{i}{1 - (1 + i)^{-n}}$$ 5. **Calculate denominator:** $$1 - (1 + 0.003833)^{-144} = 1 - (1.003833)^{-144}$$ Calculate $(1.003833)^{-144}$: $$ (1.003833)^{-144} = \frac{1}{(1.003833)^{144}} \approx \frac{1}{1.713825} = 0.583758$$ So denominator: $$1 - 0.583758 = 0.416242$$ 6. **Calculate payment $P$:** $$P = 21100 \times \frac{0.003833}{0.416242}$$ Calculate fraction: $$\frac{0.003833}{0.416242} \approx 0.009209$$ So: $$P = 21100 \times 0.009209 = 194.22$$ 7. **Final answer:** The monthly payment is approximately **194.22**. This means paying 194.22 at the end of each month for 12 years is equivalent to an immediate payment of 21100 at 4.6% interest compounded monthly.