Question

A sum of money amounts ` 7,803 for one year at the rate of 4% compounded semiannually then the sum invested is: (a) 7,000 (b) 7,500 (c) 7,750 (d) 8,000

Answer 1

the answer is (b)

solution :

let the sum be P

therefore

semi annually , rate = 4/2 = 2 percent

time = 1*2 = 2 years

amount = P ( 1+rate/100 )n

7803 = P ( 1+ 2 / 100) ki power 2

7803 = P ( 1+ 1/50 ) ki power 2

7803 = P ( 51/50 * 51/50 )

7803 = P ( 2601/ 2500 )

P = 7803 * 2500/2600

P = 3 * 2500

P = 7500

hence, P = 7500