Final answer:
The future value of $1,100 compounded quarterly at 6% for four years is $1,395.06.
Step-by-step explanation:
The student asked what the future value of $1,100 placed in a savings account for four years would be if the account pays 6.00% interest compounded quarterly. To calculate the future value of an investment, we use the formula for compound interest:
FV = P × (1 + r/n)nt
Where:
FV is the future value of the investment,
P is the principal amount ($1,100),
r is the annual interest rate (6% or 0.06),
n is the number of times the interest is compounded per year (quarterly compounding means n = 4),
t is the number of years the money is invested (4 years).
So, the calculation would be:
FV = $1,100 × (1 + 0.06/4)4×4
First, divide the annual rate by the number of compounding periods per year:
0.06/4 = 0.015
Next, add 1 to that result:
1 + 0.015 = 1.015
Now, raise this result to the power of the number of compounding periods (n×t):
1.01516 = 1.26824 (rounded to 5 decimal places)
Multiply this by the principal amount:
FV = $1,100 × 1.26824
FV = $1,395.06
Therefore, the future value of $1,100 compounded quarterly at 6% for four years is $1,395.06.