Jean invests €1,000 now and another €1,000 in a year's time. If she earns an investment return of 5% per year compounded on these investments, what will their total value be after seven years?

• A. €2,153
• B. €2,747
• C. €2,814
• D. €2,894

Answer: (B)

This question tests how compound interest accumulates when you have more than one investment started at different times. The first €1,000 is invested now and compounds for seven years, while the second €1,000 is invested after one year and compounds for six years.

Calculate the future value of each part and add them: the first grows to 1000 × (1.05)^7, the second to 1000 × (1.05)^6. The total after seven years is 1000[(1.05)^7 + (1.05)^6]. This can also be written as 1000 × (1.05)^6 × (1 + 1.05) = 1000 × (1.05)^6 × 2.05.

Numerically, (1.05)^6 ≈ 1.340095640625 and (1.05)^7 ≈ 1.40710042265625. Their sum is about 2.74719606328125, so the total value is about €2,747.19, i.e., roughly €2,747.

So the total value after seven years is approximately €2,747.