Lois invests $650 every 6 months at 4.6%/a compounded semi-annually for 25 years. How much interest will she earn after the 25th year?

To find the amount of interest Lois will earn after the 25th year, we need to calculate the future value of her investments.

To calculate the future value of an investment with compounding interest, we can use the formula:

FV = P(1 + r/n)^(nt)

Where:
FV = Future Value
P = Principal amount (initial investment, which is $650)
r = Annual interest rate (4.6% in decimal form, i.e., 0.046)
n = Number of times the interest is compounded per year (semi-annually, so 2 times a year)
t = Number of years (25 years)

Plugging in the values into the formula:

FV = 650(1 + 0.046/2)^(2*25)

Now let's calculate it step by step.

Step 1: Calculate the value inside the parentheses.
1 + 0.046/2 = 1 + 0.023 = 1.023

Step 2: Calculate the exponent.
2 * 25 = 50

Step 3: Calculate the future value (FV).
FV = 650 * (1.023)^50

Using this formula, we can determine the future value of Lois's investment after the 25th year.

Now, let's calculate it.