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Ed Sloan invests $1,600 at the beginning of each year for eight years into an account that pays 10% compounded semiannually. The value of the annuity due is (use the tables in the handbook):

Verified Answer :

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FV=PV(r+1)ⁿ
FV=Future value, or your amount of money you're going to have after 8 years.
PV=Present value, or the amount of money you have just invested.
APR=10
FV=1,600(10+1)¹⁶
FV=1,600(11)¹⁶
FV=1,600(176)
FV=$281,600

Answer:

The answer is: $39,748.80

Step-by-step explanation:

The principle amount is p = $1600  

rate is 10% or 0.10 but as its compounded semiannually it becomes,

\(\frac{0.10}{2}\) = 0.05  

n = \(8\times 2\) =16

Formula is :


\(p\frac{(1+r)^{n}-1 (1+r)}{r}\)

Putting values in formula we get

\(\frac{1600(1+0.05)^{16}-1(1+0.05) }{0.05}\)

\(\frac{1600(1.05)^{16}-1(1.05) }{0.05}\)

\(\frac{1600*(2.183-1)(1.05)}{0.05}\) = 39748.80

The value of the annuity due is $39,748.80

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