Final answer:
To calculate the future value of an investment with compound interest, we use the formula A = P(1 + r/n)^(nt). Applying this formula to Berta's investment of $100,000 at 12% interest compounded quarterly for 10 years, we find that she has accumulated approximately $310,604.72.
Step-by-step explanation:
Compound Interest Formula
The formula to calculate the future value (accumulated amount) of an investment with compound interest is:
A = P(1 + r/n)^(nt)
Where:
- A is the accumulated amount (the total value of the investment after t years)
- P is the principal amount (the initial investment)
- r is the annual interest rate (expressed as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years the money is invested
In this case, Berta invested $100,000 at 12% interest compounded quarterly for 10 years. So, the values for the formula are:
- P = $100,000
- r = 12% = 0.12
- n = 4 (compounded quarterly)
- t = 10 years
We can plug these values in and calculate the accumulated amount (A):
A = $100,000(1 + 0.12/4)^(4*10)
A = $100,000(1 + 0.03)^40
A = $100,000 * 1.03^40
Using a calculator, we find that A ≈ $310,604.72
Therefore, Berta has accumulated approximately $310,604.72 over the 10 years.