CA Foundation · Quantitative Aptitude · Mathematics of Finance
The future value of an ordinary annuity of equal annual payments, at 12% per annum compound interest, is ₹1,20,000. If the same payments for the same number of years were made at the beginning of each year (annuity due) at the same rate, what would the future value be?
The future value is ₹1,34,400. Every payment in an annuity due is made one period earlier, so each earns one more year of interest. The ordinary annuity value is therefore multiplied by (1 + i), giving 1,20,000 × 1.12 = ₹1,34,400.
- A₹1,34,400Correct
- B₹1,07,143
- C₹1,50,528
- D₹1,20,000
Explanation
Each payment of an annuity due earns interest for one more year than in the ordinary annuity. So FV(due) = FV(ordinary) × (1 + i) = 1,20,000 × 1.12 = ₹1,34,400. Dividing by 1.12 (₹1,07,143) goes the wrong way, and multiplying by 1.12² (₹1,50,528) adds two extra periods instead of one.
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