Final answer:
Using the compound interest formula, we calculate that after 10 years, Steven's account, with an initial investment of $800.00 and an annual interest rate of 2% compounded quarterly, would grow to approximately $976.90.
Step-by-step explanation:
The question is asking to calculate the future value of an initial investment of $800.00 with 2% interest, compounded quarterly, after 10 years. To find out how much will be in the account after this time, you can use the future value formula for compound interest:
FV = P ((1 + r/n)^n*t
Where:
- FV is the future value of the investment.
- 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.
Plugging in the values:
FV = 800.00((1 + 0.02/4)^(4*10)
This simplifies to:
FV = 800.00((1 + 0.005)^40
Calculating the above expression:
FV = 800.00((1 + 0.005)^40
FV = 800.00 ( 1.005 ^ 40 )
FV = 800.00 ( 1.2214 )
FV ≈ $976.90
So, after 10 years, the amount in Steven's account would be approximately $976.90.