Subjects personal finance

Monthly Savings 020E37

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Monthly Savings 020E37


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:** $$340 + 600 = 940$$ 3. **Calculate total monthly expenses:** $$200 + 75 + 80 + 50 + 100 + 140 + 100 = 745$$ 4. **Calculate monthly savings:** $$940 - 745 = 195$$ 5. **Calculate total savings after 8 months:** $$195 \times 8 = 1560$$ 6. **Calculate the 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: $$A = 1560 \times \left(1 + \frac{0.0475}{1}\right)^{1 \times 5} = 1560 \times (1.0475)^5$$ 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 $1965$.