Question

# A friend wants to borrow money from you. He states that he will pay you \$3,400...

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

Value of all future payments at 7th 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 7th 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 7th 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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