1. **Problem statement:** Husna deposits 2500 every six months into an account with 3.8% interest compounded semi-annually. We need to find: a) The total amount after 9 years and 6 months. b) The interest earned during this period. 2. **Formula used:** For regular deposits (annuity) compounded periodically, the future value $A$ is given by: $$A = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $P$ = deposit amount per period - $r$ = interest rate per period - $n$ = total number of deposits 3. **Given values:** - $P = 2500$ - Annual interest rate = 3.8%, so semi-annual rate $r = \frac{3.8}{2} \% = 1.9\% = 0.019$ - Total time = 9 years 6 months = 9.5 years - Number of periods $n = 9.5 \times 2 = 19$ 4. **Calculate total amount:** $$A = 2500 \times \frac{(1 + 0.019)^{19} - 1}{0.019}$$ Calculate $(1 + 0.019)^{19}$: $$1.019^{19} \approx 1.4357$$ So, $$A = 2500 \times \frac{1.4357 - 1}{0.019} = 2500 \times \frac{0.4357}{0.019} = 2500 \times 22.93 = 57325$$ 5. **Calculate total deposits:** Total deposits = $2500 \times 19 = 47500$ 6. **Calculate interest earned:** Interest = Total amount - Total deposits $$57325 - 47500 = 9825$$ **Final answers:** - a) Total amount after 9 years 6 months = 57325 - b) Interest earned = 9825