$1000 was invested for two years at 10% simple interest .calculate the effective rate was earned.

Question

pls check my solve

(1+0.1/2)^2-1
= 0.1025

but the true answer is 9.54%

pls help me to get the formula of effective rate

Answer 1

Interest earned was simple interest, so in two years, the future value is
1000(1+2*0.1)=1200

With compound interest of rate i, the equivalent interest would be
1000(1+i)²=1200
or
(1+i)=√(1200/1000)=1.095445
or 9.54% approx.