Final answer:
The amount accumulated after 20 years, with $1000 invested at the beginning of every six months at 8.5% compounded semiannually, is approximately $2732.86.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, you can use the compound interest formula:
A = P (1 + {r} / {n})^{nt}
where:
- A is the future value of the investment/loan, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal form).
- n is the number of times that interest is compounded per unit t (time period).
- t is the time the money is invested or borrowed for, in years.
In this case:
- P = $1000 (the amount invested at the beginning of every six months),
- r = 0.085 (8.5% interest rate in decimal form),
- n = 2 (compounded semiannually, so twice a year),
- t = 20 years.
Substitute these values into the formula:
A = 1000 (1 + {0.085} / {2}^{2 x 20}
Now, calculate (A):
A = 1000 (1 + 0.0425)^{40}
A ≈ 1000 x 2.732864
A ≈ $2732.86
So, the amount that will be accumulated after 20 years is approximately $2732.86.