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CA Foundation · Quantitative Aptitude · Mathematics of Finance

Which of the following correctly relates the future value of an annuity due (FV_due) to the future value of an ordinary annuity (FV_ord) for the same payment, rate and number of periods, with interest rate i per period?

The future value of an annuity due equals the future value of the ordinary annuity multiplied by (1 + i). Every payment is made one period earlier, so it earns one more period of interest, which scales the whole accumulated amount by the factor (1 + i).

  1. AFV_due = FV_ord × (1 + i)Correct
  2. BFV_due = FV_ord ÷ (1 + i)
  3. CFV_due = FV_ord + i
  4. DFV_due = FV_ord × (1 − i)

Explanation

In an annuity due each payment is made one period earlier than in an ordinary annuity, so each payment earns interest for one extra period. The whole future value is therefore multiplied by (1 + i). Dividing by (1 + i) would apply to present values or reduce the amount, which is wrong.

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