Q.For the same periodic payment, number of periods and interest rate, the future value of an annuity due compared with the future value of an ordinary annuity is:\n(a) equal to it\n(b) greater than it\n(c) less than it\n(d) unrelated to it

An annuity due has each payment made one period earlier than an ordinary annuity, so every payment earns interest for one extra period.

The future value of an annuity due equals that of an ordinary annuity multiplied by one extra period's growth:

Since the interest rate $i$ is positive, $(1+i) > 1$, so $A_{\\text{due}} > A_{\\text{ordinary}}$. The correct option is (b) greater than it.

Why the other options are wrong:

• (a) equal to it would require $i = 0$ (no interest), which is not an annuity problem.
• (c) less than it reverses the logic — advance payments earn more interest, not less.
• (d) unrelated is false; the two are related by the exact factor $(1+i)$. …

Some students reason that 'due' sounds like a debt and guess it should be smaller. The correct intuition is purely about timing: paying at the start of a period leaves the money invested one period longer, so an annuity due always a …