Question

What is the future value of the following cash flows at the end of year 3 if the interest rate is 7.25%? The cash flows occur at the end of each year. Year 1 $6,800 Year 2 $2,100 Year 3 $0

Answer 1

The future value of the cash flows at the end of year 3 with a 7.25% interest rate is $10,065.49.

Step-by-step explanation:

To determine the future value of cash flows at the end of year 3 with an interest rate of 7.25%, we use the formula for compound interest:

Future Value = Principal × (1 + interest rate)time

For each cash flow:

• Year 1 cash flow future value at the end of Year 3: $6,800 × (1 + 0.0725)2
• Year 2 cash flow future value at the end of Year 3: $2,100 × (1 + 0.0725)1
• Year 3 cash flow is $0, so its future value is also $0.

Now, let's calculate these:

• Year 1 future value: $6,800 × (1 + 0.0725)2 = $6,800 × 1.14900625 = $7,813.24
• Year 2 future value: $2,100 × (1 + 0.0725) = $2,100 × 1.0725 = $2,252.25
• Year 3 future value: $0 (There are no additional calculations needed for Year 3 as the cash flow is $0.)

The combined future value at the end of Year 3 is the sum of these individual future values:

$7,813.24 (Year 1) + $2,252.25 (Year 2) = $10,065.49

This amount represents the total value of the cash flows at the end of Year 3 when they are subject to compounding at an annual interest rate of 7.25%.