Question

A friend wants to borrow money from you. He states that he will pay you $3,600 every 6 months for 11 years with the first payment exactly 4 years and six months from today. The interest rate is an APR of 5.9 percent with semiannual compounding. What is the value of the payments today?

Answer #1

Here the problem needs two steps to solve.

First find the Present value of the amount after 4 years and six months.This can be found by using PV function in EXCEL

=PV(rate,nper,pmt,fv,type)

Here the interest is semi-annual compounding

rate=5.9%/2=2.95%

nper=2*11=22

pmt=3600

fv=0

=PV(2.95%,22,3600,0,0)

PV=$57,661.34

Again this amount, $57,661.34 has to discounted today from 4 and 6 months time

Value of today=PV/((1+r)^n)

r=2.95%

n=number of periods=9 (4 and 6 months =Total 9 periods)

Value of today=$57,661.34/((1+2.95%)^9)=$44,386.16

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