Question 1190335: 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
Answer by math_tutor2020(3816)   (Show Source):
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Apply the future value of annuity due formula (not the regular future value annuity).
The "due" is because each deposit is made at the beginning of the period. If the deposits were made at the end of the period, after the compounding gets a chance to happen, then we'd use a regular future value annuity formula.
The formula we use is
FV = P(1+i)*( (1+i)^n - 1 )/i
where,
FV = future value of the money after n periods
P = deposit per period
i = interest rate per period (in decimal form)
n = number of periods
We have the following items
P = 3000
i = 0.10/2 = 0.05
n = 2*12 = 24
So,
FV = P(1+i)*( (1+i)^n - 1 )/i
FV = 3000*(1+0.05)*( (1+0.05)^24 - 1 )/0.05
FV = 140,181.296453963
FV = $140,181.30
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