To solve the problem, let's break it into steps:

Key Information:

• Monthly Deposit ($P$) = $300
• Annual Interest Rate ($r$) = 4% = 0.04
• Compounding Periods per Year = 12 (monthly)
• Time Period ($t$) = 20 years

Formula for Future Value of a Series (Compound Interest):

The formula for the future value of monthly deposits is: $FV = P \cdot \frac{(1 + \frac{r}{n})^{n \cdot t} - 1}{\frac{r}{n}}$ Where:

• $P$ = monthly deposit
• $r$ = annual interest rate
• $n$ = compounding periods per year
• $t$ = total time in years

Now, let's calculate each part:

(a) How much will you have in the account in 20 years?

$FV = 300 \cdot \frac{(1 + \frac{0.04}{12})^{12 \cdot 20} - 1}{\frac{0.04}{12}}$

(b) Total money deposited into the account:

The total money deposited is simply: $\text{Total Deposits} = P \cdot n \cdot t$

(c) Total interest earned:

$\text{Interest} = \text{Future Value} - \text{Total Deposits}$

Let me calculate these values for you.# Given values P = 300 # monthly deposit in dollars r = 0.04 # annual interest rate (4%) n = 12 # number of compounding periods per year (monthly) t = 20 # time in years

Future Value calculation

FV = P * (((1 + r / n)**(n * t) - 1) / (r / n))

Total money deposited

total_deposits = P * n * t

Total interest earned

total_interest = FV - total_deposits

FV, total_deposits, total_interest(110032.38782697874, 72000, 38032.38782697874)(110032.38782697874, 72000, 38032.38782697874)success### Results: (a) Amount in the account in 20 years: $110,032.39
(b) Total money deposited into the account: $72,000
(c) Total interest earned: $38,032.39

Would you like more details on the calculations or assistance with related questions?

Here are 5 related questions you might explore:

1. How does changing the monthly deposit affect the final amount?
2. What if the interest was compounded quarterly instead of monthly?
3. How would a higher annual interest rate (e.g., 6%) impact the final amount?
4. How much time would it take to reach $150,000 with the same monthly deposit?
5. How does compounding frequency affect interest growth over time?

Tip: Consistent savings, even with small amounts, can grow significantly over time due to compound interest!