If the next year's dividend D1 equals D0 times (1 plus growth g), which of the following expresses D1 given D0 and g?

If the next year's dividend D1 equals D0 times (1 plus growth g), which of the following expresses D1 given D0 and g?

• A. D1 equals D0+g
• B. D1 equals D0*(1+g)
• C. D1 equals D0*(1-g)
• D. D1 equals D0/g

Answer: (B)

The idea is that next year's dividend grows from the current dividend by a growth rate g. This means you multiply the current dividend by the factor (1 plus g). So D1 = D0 × (1 + g). If g is a decimal, for example 0.05, then D1 = D0 × 1.05 (a 5% increase). If you instead tried D1 = D0 + g, you’d be adding a fixed amount g rather than applying a percentage growth, which isn’t what a growth rate represents. D1 = D0 × (1 − g) assumes a decrease, not growth, and D1 = D0 ÷ g scales by the reciprocal of g, not by the growth factor. For a concrete check, if D0 = $2 and g = 0.03, D1 = $2 × 1.03 = $2.06.

The idea is that next year's dividend grows from the current dividend by a growth rate g. This means you multiply the current dividend by the factor (1 plus g). So D1 = D0 × (1 + g). If g is a decimal, for example 0.05, then D1 = D0 × 1.05 (a 5% increase). If you instead tried D1 = D0 + g, you’d be adding a fixed amount g rather than applying a percentage growth, which isn’t what a growth rate represents. D1 = D0 × (1 − g) assumes a decrease, not growth, and D1 = D0 ÷ g scales by the reciprocal of g, not by the growth factor. For a concrete check, if D0 = $2 and g = 0.03, D1 = $2 × 1.03 = $2.06.