Question

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 1

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 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 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