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 _________. *
Answers
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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