Final answer:
The future value of Spencer's account after 9 years, with a 3% annual compound interest, is $803.57.
Step-by-step explanation:
Spencer wants to calculate the future value of a $600.00 investment into an account with a 3% annual compound interest rate over a period of 9 years. To find out the amount in the account after 9 years, the formula for compound interest is used:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money).
r = the annual interest rate (decimal).
n = the number of times that interest is compounded per year.
t = the time the money is invested or borrowed for, in years.
In Spencer's case:
P = $600
r = 3% or 0.03
n = 1 (since the interest is compounded annually)
t = 9 years
Let's plug these values into the formula:
A = 600(1 + 0.03/1)^(1*9)
A = 600(1 + 0.03)^9
A = 600(1.03)^9
A = $803.57
Thus, after 9 years, Spencer will have $803.57 in the account.