Mr. Ahmed invested an amount at the rate r compounded semi-annually. what value of r will ensure the interest is amount double the amount invested after a year?

Answer 1

If we invest $1. in 6 months we will have 1+r/2 dollars. Both the original dollar plus the interest earned in the first six months will earn interest over the next 6 months. So after 1 year we will have (1+R/2)^2 DOLLARS. We want that value to double sooooooo,

(1+r/2)^2 =2 Take the square root of both sides

(1+r/2) =sqrt(2) or r/2 = (sqrt(2)-1) so r = 2(sqrt(2)-1)) so r=82.84%