Q8. The present value of an annuity of Rs. 1,331 paid at the end of each year for 3 years, at 10 % p.a. is _________. *​

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1. Given : an annuity of Rs. 1,331 paid at the end of each year for 3 years, at 10 % p.a.

   To Find : Present Value

   Solution:

   Let say Present Value = 1000x Rs

   interest in 1st Year = (10/100)1000x = 100x Rs

   Paid = 1331 Rs

   Remaining = 1000x + 100x – 1331 Rs

   = 1100x – 1331 Rs

   Interest in 2nd year = (1100x – 1331) * 10 /100 = 110x – 133.1 Rs

   Paid = 1331 Rs

   Remaining = 1100x – 1331 + 110x – 133.1 – 1331

   = 1210x – 2,795.1

   Interest in 3rd year = (1210x – 2,795.1 ) * 10 /100

   ( 1210x – 2,795.1 ) + (1210x – 2,795.1 ) 0.1 = 1331

   => ( 1210x – 2,795.1 )1.1 = 1331

   => 1210x – 2,795.1 = 1,210

   => 1210 ( x – 1) = 2,795.1

   => x – 1 = 2.31

   => x = 3.31

   => 1000x = 3310

   The present value = 3310 Rs

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