Question

Use the following timeline to answer the​ question(s) below.

This timeline goes from years 0 to 3. In time equals 0, there is no cash flow. In time equals 1, there is a cash inflow of 600 dollars. In time equals 2, there is a cash inflow of 1200 dollars. In time equals 3, there is a cash inflow of 1800 dollars.
At an annual interest rate of​ 7%, the future value of this timeline in year 3 is closest​ to:
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Part 1
A.$3295.
B.​$3771.
C.​$3600.
D.​$4035.

Answer 1

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.