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Future Value Annuity

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Future Value Annuity


1. **State the problem:** You save R2525 every month at the end of each month for 3 years. The bank pays 13.5% interest per annum compounded monthly. You want to find out how much money you can withdraw at the end of 3 years. 2. **Identify the variables:** - Monthly payment, $P = 2525$ - Annual interest rate, $r = 13.5\% = 0.135$ - Number of years, $t = 3$ - Number of months, $n = 3 \times 12 = 36$ - Monthly interest rate, $i = \frac{r}{12} = \frac{0.135}{12} = 0.01125$ 3. **Use the future value of an ordinary annuity formula:** $$FV = P \times \frac{(1 + i)^n - 1}{i}$$ 4. **Calculate the future value:** $$FV = 2525 \times \frac{(1 + 0.01125)^{36} - 1}{0.01125}$$ 5. Calculate $(1 + 0.01125)^{36}$: $$1.01125^{36} \approx 1.488864$$ 6. Substitute back: $$FV = 2525 \times \frac{1.488864 - 1}{0.01125} = 2525 \times \frac{0.488864}{0.01125}$$ 7. Simplify: $$ \frac{0.488864}{0.01125} \approx 43.432$$ 8. Final value: $$FV = 2525 \times 43.432 \approx 109,640.8$$ **Answer:** You can withdraw approximately $109,640.80$ at the end of 3 years.