CA Foundation · Quantitative Aptitude · Mathematics of Finance
Anil wants ₹2,31,000 at the end of 2 years. He will deposit an equal sum at the end of every half-year for 2 years (4 deposits) in an account paying 20% per annum compounded half-yearly. Using (1.1)^4 = 1.4641, what is the required half-yearly deposit, to the nearest rupee?
The required half-yearly deposit is about ₹49,774. With a 10% half-yearly rate and 4 deposits at period end, the annuity factor is (1.4641 − 1)/0.1 = 4.641, so the deposit is 2,31,000 divided by 4.641.
- A₹49,774
- B₹50,000Correct
- C₹45,249
- D₹55,000
Explanation
Half-yearly rate = 10%. Annuity factor = (1.4641 − 1)/0.1 = 4.641. Deposit = 2,31,000/4.641 = ₹49,774. Check: 49,774 × 4.641 ≈ 2,31,000. ₹45,249 would result from using an annuity-due factor (5.1051), a wrong timing assumption.
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