To have future value of $130,000 at the end of 20 years, the payments that should be deposited at the beginning of each 6-month period is $1,796.15
Since the payment is made at the beginning of each period (6 months), the type of the annuity is the annuity due. The formula for the future value of an annuity due is given by:
FV = PMT [(1 + r)ⁿ - 1] · (1 + r) / r
Where:
FV = future value
PMT = annuity payment
r = interest rate per period
n = number of periods
Parameters given from the problem:
FV = 130,000
r = 5.4%/2 = 2.7% = 0.027
n = 20 years x 2 = 40
Plug these parameters into the formula:
130,000 = PMT [(1 + 0.027)⁴⁰ - 1] . (1 + 0.0027) / 0.027
PMT = 3.51 / [(1.027⁴⁰ - 1) x 1.027] = 1,796.15
Hence, the amount of payment should be made is $1,796.15 each 6 months.
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