Answer:
1. To calculate the total balance in the account after 40 years, we need to find the future value of Raul's monthly contributions using the formula for compound interest. The formula is:
FV = Pmt x ( ((1 + r/n)^(n*t) - 1) / (r/n) )
where FV is the future value, Pmt is the monthly payment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, Raul contributes $100 per month, or $1,200 per year. The interest rate is 1.5%, or 0.015 as a decimal. The interest is compounded once per year, so n = 1. The time period is 40 years.
Plugging these values into the formula, we get:
FV = 1200 x ( ((1 + 0.015/1)^(1*40) - 1) / (0.015/1) )
FV = $73,893.40
Therefore, the total balance in the account after 40 years is $73,893.40.
2. Raul contributed $100 per month for 40 years, or a total of:
$100 x 12 x 40 = $48,000
Therefore, Raul contributed $48,000 himself.
3. To find the amount of money Raul made through compound interest, we need to subtract the amount he contributed from the total balance in the account. The amount of interest earned is:
$73,893.40 - $48,000 = $25,893.40
Therefore, Raul made $25,893.40 through compound interest in this savings account.
4. One way Raul could have increased the total amount of money he made over the 40 years is by investing in a diversified portfolio of stocks and bonds. While investing comes with greater risk, it also offers the potential for higher returns. Over a long period of time like 40 years, the stock market historically has provided higher returns than savings accounts. By investing in a diversified portfolio, Raul could have potentially earned a higher return than his savings account, while still minimizing his risk through diversification.