Final answer:
After 6 years, a $1000 investment at a 10.5% interest rate compounded every 4 months would grow to $1,946.08, demonstrating the impact of compound interest on investments over time.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In this case, P is $1000, r is 10.5% or 0.105, n is 3 (since interest is compounded every 4 months, or three times a year), and t is 6 years.
Plugging in the values we get:
A = 1000(1 + 0.105/3)^(3*6)
A = 1000(1 + 0.035)^(18)
A = 1000(1.035)^18
A = 1000 * 1.94608
A = $1,946.08
Therefore, after 6 years, $1000 invested at 10.5% interest compounded every 4 months would be worth $1,946.08.