1. **State the problem:** James saves 140 every month for 4 years in a bank account with an interest rate of 4.40% compounded monthly. We need to find: a. The accumulated value of his savings at the end of 4 years. b. The interest earned over the 4 years. 2. **Formula used:** For monthly compounding with regular monthly deposits, the future value of an annuity formula is: $$A = P \times \frac{(1 + r)^n - 1}{r}$$ where: - $A$ is the accumulated amount after $n$ months, - $P$ is the monthly deposit, - $r$ is the monthly interest rate (annual rate divided by 12), - $n$ is the total number of deposits (months). 3. **Calculate values:** - Annual interest rate = 4.40% = 0.044 - Monthly interest rate $r = \frac{0.044}{12} = 0.0036667$ - Number of months $n = 4 \times 12 = 48$ - Monthly deposit $P = 140$ 4. **Calculate accumulated value:** $$A = 140 \times \frac{(1 + 0.0036667)^{48} - 1}{0.0036667}$$ Calculate $(1 + 0.0036667)^{48}$: $$ (1.0036667)^{48} \approx 1.191123$$ Substitute back: $$A = 140 \times \frac{1.191123 - 1}{0.0036667} = 140 \times \frac{0.191123}{0.0036667}$$ Simplify fraction: $$\frac{0.191123}{0.0036667} \approx 52.103$$ So, $$A = 140 \times 52.103 = 7294.42$$ Rounded to nearest cent, accumulated value is **7294.42**. 5. **Calculate interest earned:** Total amount deposited = $140 \times 48 = 6720$ Interest earned = Accumulated value - Total deposits $$7294.42 - 6720 = 574.42$$ So, interest earned is **574.42**. **Final answers:** - a. Accumulated value = 7294.42 - b. Interest earned = 574.42