Sandra deposits $3,000 at the beginning of each semiannual period for 12 years at 10% interest compounded semiannually. determine the amount she will have in the account after 12 years. round to the nearest cent. a. $130,506.00 c. $121,291.43 b. $140,181.30 d. $70,568.14

Annuity formula for depositing at the end of each period.
Future value, 
F=A*((1+i)^n-1)/i
A=deposit per period, $3000 
i=interest per period, 10%/2 = 5% = 0.05 per half year
n=number of periods = 12 years = 24 half-years

If the deposit is at the beginning of each period, then
we can use the above formula, with 25 periods, but skipping the final payment, i.e.
F=A*((1+i)^(n+1)-1)/i-A
=3000*((1+.1/2)^(24+1)-1)/(.1/2) - 3000
=143181.296 - 3000
=143181.30 -3000
=140181.30 (to the nearest cent)

128/3reason being 5 and 1/3 = 16/316/3 • 2/3 = 32/31 and 1/3 = 4/3 32/3 • 4/3 this will equal 128/3