Question : What is the present value of Rs. 10,000 received in 2 years if the interest rate is 12% per year discounted semi-annually?
Option 1: Rs. 7,020.94
Option 2: Rs. 7,900.90
Option 3: Rs. 7,920.94
Option 4: Rs. 7,900.94
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Correct Answer: Rs. 7,920.94
Solution :
Amount, $A=10000$
Rate of interest, $R=$ 6% (semi-annually)
Period in years = 2 years
Period computed semi-annually, $n=4$
Thus, total amount after $n$ time periods at $R$% rate of interest, $A$ = $P[1+\frac{R}{100}]^n$
So, $10000=P[1+\frac{6}{100}]^4$
⇒ $10000=P[\frac{106}{100}]^4$
⇒ $P=7920.94$
Hence, the correct answer is Rs. 7920.94.
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