1. **Problem Statement:** Nurin saves RM12,000 at age 22 in an account with 4.8% annual interest compounded monthly. After 3 years, she adds RM5,500 more. She plans to buy an apartment at age 27 (5 years after initial deposit). Calculate the total amount at age 27, total interest earned, and check if she has enough for RM25,000 deposit. 2. **Formula for compound interest:** $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where $A$ is the amount, $P$ is principal, $r$ is annual interest rate (decimal), $n$ is compounding periods per year, and $t$ is time in years. 3. **Step 1: Calculate amount after 3 years for first deposit** - $P = 12000$ - $r = 0.048$ - $n = 12$ - $t = 3$ $$A_1 = 12000 \left(1 + \frac{0.048}{12}\right)^{12 \times 3} = 12000 \left(1 + 0.004\right)^{36}$$ Calculate: $$A_1 = 12000 \times (1.004)^{36}$$ 4. **Step 2: Calculate amount of $A_1$ after 2 more years (until age 27)** - $t = 2$ $$A_1' = A_1 \left(1 + \frac{0.048}{12}\right)^{12 \times 2} = A_1 \times (1.004)^{24}$$ 5. **Step 3: Calculate amount of second deposit after 2 years** - $P = 5500$ - $t = 2$ $$A_2 = 5500 \left(1 + \frac{0.048}{12}\right)^{24} = 5500 \times (1.004)^{24}$$ 6. **Step 4: Calculate total accumulated amount at age 27** $$A_{total} = A_1' + A_2$$ Calculate powers: $$(1.004)^{36} \approx 1.1616$$ $$(1.004)^{24} \approx 1.1005$$ Calculate intermediate amounts: $$A_1 = 12000 \times 1.1616 = 13939.2$$ $$A_1' = 13939.2 \times 1.1005 = 15334.7$$ $$A_2 = 5500 \times 1.1005 = 6052.75$$ Total amount: $$A_{total} = 15334.7 + 6052.75 = 21387.45$$ 7. **Step 5: Calculate total interest earned** Total principal deposited: $$12000 + 5500 = 17500$$ Interest earned: $$21387.45 - 17500 = 3887.45$$ 8. **Step 6: Check if Nurin has enough for RM25,000 deposit** Since $21387.45 < 25000$, Nurin does not have enough savings for the deposit. **Final answers:** - Total accumulated amount: **21387.45** - Total interest earned: **3887.45** - Nurin does not have enough savings for the RM25,000 deposit.