Question

In what time will Rs. 1,500 yield Rs. 496.50 as compound interest at 20% per year compounded half-yearly ?

Answer 1

Given: P=Rs. 1,500; C.I.= Rs. 496.50 and r = 20%
Since interest is compounded semi-annually

Then, C.I. = `"P"[( 1 + r/[2 xx 100])^(n xx 2) - 1]`

⇒ 496.50 = 1,500`[( 1 + 20/[2 xx 100])^(n xx 2) - 1]`

⇒ `[496.50]/[1500] = (11/10)^(2n) - 1`

⇒ `331/1000 + 1 = (11/10)^(2n)`

⇒ `1331/1000 = (11/10)^(2n)`

⇒ `(11/10)^3 = (11/10)^(2n)`

On comparing, we get,

2n = 3 ⇒ n = `1 1/2` years