Teach2Fish Savings
1. **Problem statement:** We analyze the Teach2Fish group's monthly deposits and interest earnings from the table and calculate their total savings after 3 years with 5.7% annual interest compounded annually.
2. **Monthly deposit amount:** Each of the 11 members donates 150 monthly.
3. **Calculate total monthly deposit:**
$$\text{Total deposit} = 11 \times 150 = 1650$$
4. **Deposit day:** From the table, the amount in the account on the first day of January is 1650, which matches the total deposit, so deposits are made on the first day of each month.
5. **Interest rate and compounding:** Interest rate is 5.7% per annum compounded annually.
6. **Calculate total savings after 3 years:**
- Monthly deposits: 1650
- Number of years: 3
- Annual interest rate: 5.7% or 0.057
7. **Formula for future value of an annuity with annual compounding:**
$$FV = P \times \frac{(1 + r)^n - 1}{r}$$
where
- $P$ = annual deposit
- $r$ = annual interest rate
- $n$ = number of years
8. **Convert monthly deposits to annual deposits:**
$$P = 1650 \times 12 = 19800$$
9. **Calculate future value:**
$$FV = 19800 \times \frac{(1 + 0.057)^3 - 1}{0.057}$$
10. **Calculate powers and subtraction:**
$$ (1 + 0.057)^3 = 1.057^3 = 1.1807$$
$$ 1.1807 - 1 = 0.1807$$
11. **Calculate fraction:**
$$ \frac{0.1807}{0.057} = 3.169$$
12. **Calculate final amount:**
$$ FV = 19800 \times 3.169 = 62716.2$$
13. **Answer:** After 3 years, the group would have saved approximately **62716.20**.