Charlie invests €1200 at 3.5% per annum compound interest. After how many years will his investment reach at least €2000?

Answer

To find out how many years it will take for Charlie's investment to grow to at least €2000, we can use the formula for compound interest: A = P(1 + r/n)^(nt) Where: - A = the future value of the investment/loan, including interest - P = the principal investment amount (€1200) - r = the annual interest rate (decimal) (3.5% = 0.035) - n = the number of times that interest is compounded per year (assuming 1 for annual compounding) - t = the number of years the money is invested or borrowed for In this case: - A = €2000 - P = €1200 - r = 0.035 - n = 1 Substituting the known values into the formula: €2000 = €1200(1 + 0.035/1)^(1*t) This simplifies to: €2000 = €1200(1.035)^t To isolate (1.035)^t, we can divide both sides by €1200: (1.035)^t = €2000/€1200 (1.035)^t = 1.6667 Next, we need to solve for t using logarithms: t = log(1.6667) / log(1.035) Calculating the logarithms: log(1.6667) ≈ 0.2198 log(1.035) ≈ 0.0152 Now, divide the two results: t ≈ 0.2198 / 0.0152 ≈ 14.45 Since t must be a whole number (you can't invest for a fraction of a year in practical terms), we round 14.45 up to 15. Thus, it will take Charlie approximately 15 years for his investment to reach at least €2000.