Which is the best investment for three consecutive years?

a. A growth of 5% followed by a growth of 10% followed by a growth of 15%
b. A growth of 15% followed by a growth of 10% followed by a growth of 5%
c. Three years of growth at 10% per year.

evaluate:

a) 1.05(1.1)(1.15)
b) 1.15(1.1)(1.05)
c) 1.1(1.1)(1.1) and compare

To determine the best investment option for three consecutive years, we need to calculate the total return (or end value) of each option.

Option a: A growth of 5% followed by a growth of 10% followed by a growth of 15%
To calculate the end value, we calculate each year's return on the previous year's investment and add it to the previous year's total.

Year 1: The initial investment grows by 5%. The end value is (1 + 0.05) = 1.05 times the initial investment.
Year 2: The previous year's end value grows by 10%. The end value is (1.05 * 1.1) = 1.155 times the initial investment.
Year 3: The previous year's end value grows by 15%. The end value is (1.155 * 1.15) = 1.32625 times the initial investment.

Option b: A growth of 15% followed by a growth of 10% followed by a growth of 5%
Using the same method as above:

Year 1: The initial investment grows by 15%. The end value is (1 + 0.15) = 1.15 times the initial investment.
Year 2: The previous year's end value grows by 10%. The end value is (1.15 * 1.1) = 1.265 times the initial investment.
Year 3: The previous year's end value grows by 5%. The end value is (1.265 * 1.05) = 1.32825 times the initial investment.

Option c: Three years of growth at 10% per year
Here, we can calculate the end value directly:

End value = (1 + 0.10)^3 = 1.10 * 1.10 * 1.10 = 1.331 times the initial investment.

Comparing the end values:
- Option a: 1.32625 times the initial investment
- Option b: 1.32825 times the initial investment
- Option c: 1.331 times the initial investment

Based on the calculations, option c (Three years of growth at 10% per year) provides the highest end value. Therefore, option c is the best investment option for three consecutive years.