Question

What is the price of a monthly bond (makes payments monthly) that has 20 years to maturity, a coupon rate of 12.00%, and a face value of $1,000 if your required rate of return is an APR of 18.00% with quarterly compounding?

Answer 1

Quarterly Rate = 18% / 4

= 4.5%

Monthly Rate :

Particulars	Amount
Effective Annual rate	4.5000%
No. of periods per anum	3.0000

APR = [ [ ( 1 + EAR )^( 1 / n ) ] - 1 ]
= [ [ ( 1 + 0.045 )^( 1 / 3 ) ] - 1 ]
= [ [ ( 1.045 )^( 1 / 3 ) ] - 1 ]
= [ [ 1.0148 ] - 1 ]
= 0.0148 I.e 1.48%

Bond Price:
It refers to the sum of the present values of all likely coupon payments plus the present value of the par value at maturity. There is inverse relation between Bond price and YTM ( Discount rate ) and Direct relation between Cash flow ( Coupon/ maturity Value ) and bond Price.

Price of Bond = PV of CFs from it.

Period	Cash Flow	%PVF/ PVAF @1.48%	PV of CFs
1-240	$                   10.00	65.5795	$                 655.80
240	$             1,000.00	0.0294	$                   29.42
Bond Price			$                 685.22

As Coupon Payments are paid periodically with regular intervals, PVAF is used.
Maturity Value is single payment. Hence PVF is used.

Periodic Cash Flow = Annual Coupon Amount / No. times coupon paid in a year
Disc Rate Used = Disc rate per anum / No. of times coupon paid in a Year

What is PVAF & PVF ???
PVAF = Sum [ PVF(r%, n) ]
PVF = 1 / ( 1 + r)^n
Where r is int rate per Anum
Where n is No. of Years

How to Calculate PVAF using Excel ???
+PV(Rate,NPER,-1)
Rate = Disc rate
Nper = No. of Periods