In what time will Rs 64000 amount to Rs 68921 at 5% per annum, interest being compounded half-yearly?

Explanation

Let the time be ` n`
Principal `P=Rs. 64000`
Amount `A=Rs. 68921`
Rate `R=5% `per annum or `5/2` per half-yearly
`A=P{1+R/(2times100)}^n`
`68921=64000(1+5/200)^(2n)`
`68921/64000=(41/40)^(2n)`
`(41/40)^3=(41/40)^(2n)`
On comparing
both the sides, we get:
`3=2n`
`n=3/2years=1 1/2 `years
`therefore` The time `=1 1/2` years.