CA Foundation · Quantitative Aptitude · Mathematics of Finance
Mehta Industries wants to accumulate ₹3,64,100 at the end of 3 years to replace equipment. It will make three equal deposits at the beginning of each year in a fund earning 10% per annum compounded annually. What should be each deposit?
Each deposit should be ₹1,00,000. For an annuity due, the future value equals the deposit times the ordinary annuity factor of 3.31 times a further 1.1, which is 3.641. Dividing 3,64,100 by 3.641 gives ₹1,00,000. Treating deposits as year-end gives the wrong ₹1,10,000.
- A₹90,909
- B₹1,00,000Correct
- C₹1,10,000
- D₹1,21,367
Explanation
For deposits at the beginning of each year, FV = A x [(1.1)^3 - 1]/0.1 x 1.1 = A x 3.31 x 1.1 = 3.641A. So A = 3,64,100 / 3.641 = ₹1,00,000. ₹1,10,000 results from treating the deposits as end-of-year (3,64,100 / 3.31), ignoring the extra year of interest.
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