Semiannually compound interest

If you deposit $5000 into an account paying 8.25% annual interest compounded semiannually, how long until there is $9350 in the account?

Correct result:

t =  96 m

Solution:

p=8.25%=8.25100=0.0825 i=1+p/2=1+0.0825/2=833800≐1.0413  5000⋅ in=9350 in=9350/5000  nlog⁡i=log⁡9350/5000  n=log⁡(9350/5000)log⁡(i)=log⁡(9350/5000)log⁡(1.0413)≐15.4851 n1=⌈n⌉=⌈15.4851⌉=16  t=12/2⋅ n1=12/2⋅ 16=96 m

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