Sure, let's solve this step-by-step.
To determine the present value (PV) of a future amount of money, we use the formula:
[tex]\[ PV = \frac{FV}{(1 + i)^n} \][/tex]
where:
- [tex]\( FV \)[/tex] is the future value,
- [tex]\( i \)[/tex] is the annual interest rate, and
- [tex]\( n \)[/tex] is the number of years.
In this problem:
- The future value ([tex]\( FV \)[/tex]) is [tex]$1,100,
- The annual interest rate (\( i \)) is 2%, which is 0.02 when expressed as a decimal,
- The number of years (\( n \)) is 6.
Now, let's apply the values to the formula:
\[ PV = \frac{1100}{(1 + 0.02)^6} \]
First, calculate the factor \( (1 + i)^n \):
\[ (1 + 0.02)^6 = 1.02^6 \]
Then calculate the present value:
\[ PV = \frac{1100}{1.02^6} \]
After performing the calculation, the present value (`PV`) is approximately $[/tex]976.77.
Therefore, the present value of [tex]$1,100 to be received in six years at an annual interest rate of 2% is:
\[ \boxed{976.77} \]
The correct answer from the provided options is $[/tex]976.77.
