Question

Sandra deposits $3,000 at the end 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.
$133,506.00
b.
$140,181.30
c.
$121,291.43
d.
$70,568.14

Answer 1

Future value of an ordinary annuity:
S = R * [((1 + i)^n − 1) / i]

Here R = 3000, i = 0.10/2 = 0.05, n = 12*2 = 24:
(1.05)^24 ≈ 3.225099943
S = 3000 * [(3.225099943 − 1) / 0.05] ≈ 3000 * 44.50199886 ≈ 133,505.9966

Rounded to the nearest cent: $133,506.00 — answer (a).