A friend wants to borrow money from you. He states that he will pay you $3,400 every 6 months for 9 years with the first payment exactly 7 years and six months from today. The interest rate is 5.7 percent compounded semiannually. What is the value of the payments today?
$32,128.58
$33,021.49
$35,079.17
$31,070.77
$31,956.28
Answer: $31,956.28
Value of all future payments at 7^{th} year end:
Using financial calculator BA II Plus  Input details: 
# 
I/Y = Rate/Frequency = 5.7/2 = 
2.850000 
PMT = 
$3,400.00 
N = Number of years x frequency = 9 x 2 = 
18 
FV = Future Value = 
$0.00 
CPT > PV = Value at 7^{th} year end = 
$47,360.52 
Formula based present value of annuity: 

PV = PMT x ((1(1+R%)^N)/R% = 
$47,360.52 
Now, we can calculate the present value today:
PV today = Value at end of 7^{th} year / (1+Rate/2)^(7 x 2)
PV today = $47,360.52 / (1+5.7%/2)^(7 x 2)
PV today = $31,956.29 or ~ $31,956.28
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