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 $1965$.