Final answer:
The future value of $3,078 invested for 8 years at 6% interest compounded annually is approximately $4,909.08, calculated using the compound interest formula.
Step-by-step explanation:
The future value of an investment is the amount of money to which an initial deposit will grow over time when it is placed in an account that compounds at a certain rate of interest. To calculate the future value of $3,078 invested for 8 years at 6 percent compounded annually, we use the compound interest formula:
FV = P(1 + r/n)^(nt)
Where:
- FV = future value of the investment
- P = principal amount ($3,078)
- r = annual interest rate (6% or 0.06)
- n = number of times interest is compounded per year (1 for annually)
- t = number of years the money is invested (8)
Plugging in the values, we get:
FV = $3,078(1 + 0.06/1)^(1 * 8)
FV = $3,078(1 + 0.06)^8
FV = $3,078(1.06)^8
FV = $3,078 * 1.593848
FV = $4,909.08 (rounded to two decimal places)
The future value of $3,078 invested for 8 years at a 6% annual interest rate, compounded annually, is approximately $4,909.08.