Subjects personal finance

Janette Savings F3C83F

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Janette Savings F3C83F


1. **State the problem:** Janette receives a monthly allowance of 340 and earns 600 from a part-time job. She has monthly expenses: 200 rent, 75 car insurance, 80 clothes, 50 personal care, 100 entertainment, 140 eating out, and 100 other spending. We need to find how much she can save in 8 months and then calculate the balance of that savings after 5 years at 4.75% annual interest compounded annually. 2. **Calculate total monthly income:** $$\text{Income} = 340 + 600 = 940$$ 3. **Calculate total monthly expenses:** $$\text{Expenses} = 200 + 75 + 80 + 50 + 100 + 140 + 100 = 745$$ 4. **Calculate monthly savings:** $$\text{Savings per month} = \text{Income} - \text{Expenses} = 940 - 745 = 195$$ 5. **Calculate total savings in 8 months:** $$\text{Total savings} = 195 \times 8 = 1560$$ 6. **Calculate balance after 5 years with compound interest:** Formula for compound interest: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ Where: - $P = 1560$ (principal) - $r = 0.0475$ (annual interest rate) - $n = 1$ (compounded annually) - $t = 5$ years Calculate: $$A = 1560 \left(1 + \frac{0.0475}{1}\right)^{1 \times 5} = 1560 \times (1.0475)^5$$ Calculate $(1.0475)^5$: $$1.0475^5 \approx 1.2597$$ So: $$A \approx 1560 \times 1.2597 = 1965.13$$ 7. **Round the answers:** - Total savings after 8 months: 1560 - Balance after 5 years: 1965 **Final answers:** Janette can put aside 1560 in 8 months. The balance of the account after 5 years will be approximately 1965.