In what time will * 1500 yield 496.50 Ascompound interest at 20% per Yearcompounded half yearly?

Let the time period be T years.

Given, P = Rs 1500, C.I. = Rs 496.50, R = 20% p.a. compounded semi-annually.

Thus, the time period is 1 year 6 months.

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