Final answer:
The future value in year 3, calculated by compounding the cash inflows at a 7% interest rate for the relevant years and then summing them up, is closest to $3771.
Step-by-step explanation:
To calculate the future value of cash flows at an annual interest rate of 7%, we will apply the formula Future Value = Principal × (1 + interest rate)time. We do this for each cash inflow at different times and then sum them up to find the total future value in year 3.
- Year 1: The future value of the $600 inflow after two years (year 3 - year 1) is $600 × (1 + 0.07)2 = $600 × 1.1449 = $686.94.
- Year 2: The future value of the $1200 inflow after one year (year 3 - year 2) is $1200 × (1 + 0.07)1 = $1200 × 1.07 = $1284.
- Year 3: The $1800 inflow is already in year 3, so it doesn't need to be compounded. Its future value is just $1800.
Add these values together: $686.94 + $1284 + $1800 = $3770.94.
So, The future value in year 3 is closest to $3771, which corresponds to option B.
To find the future value of the cash flows, we need to use the formula for compound interest: Future Value = Principal x (1 + interest rate)^time. We have three cash inflows at time 1, 2, and 3, which are $600, $1200, and $1800 respectively. The interest rate is given as 7% per annum. Plugging in the values into the formula:
Future Value = 600 x (1 + 0.07)^1 + 1200 x (1 + 0.07)^2 + 1800 x (1 + 0.07)^3
Calculating this expression will give us the future value of the cash flows in year 3.