Periodic Payment/Lump Sum - Market rate greater than face rate

[tpickens166]

I've been having an incredibly hard time with a problem for the last hour.

I'm trying to find the present value on a $500,000 note that has an 8% face value interest rate but a 9% market interest rate.

FV: $500,000 (due at end of 4 years)
Annuity payments: $20,000 semi-annually (total number of payments: 8)

I've calculated the present values using time value of money tables and came up with the following:

$20,000 * 5.5348 (Present value of an annuity) = 110,696
$500,000 * 0.5019 (Present value of $1) = 250,950

250,950+110,696 = 361,646

I know the answer is actually 483,510.28 but I can't figure out what I'm doing wrong.

Any help would be greatly appreciated!!

 

[bklynboy]

The amount you have for the PV of the 500K is incorrect. The amount I come up with is 354,212.61. This is calculated as (1/(1+0.09)^4)*500,000. You should check the factor you came up with. I also get 110,696 for the PV of an annuity. However, together I dont get the 483,510 you believe is the result. Not sure where I am off but perhaps someone else can assist.

 

[Triest123]

The amount you have for the PV of the 500K is incorrect. The amount I come up with is 354,212.61. This is calculated as (1/(1+0.09)^4)*500,000. You should check the factor you came up with. I also get 110,696 for the PV of an annuity. However, together I dont get the 483,510 you believe is the result. Not sure where I am off but perhaps someone else can assist.

=> Since the annuity payments is $20,000 semi-annually, so the discounted rate
is 9%/2 = 4.5%.

PV for the annuity : $131,917.72
PV for $500,000 : $354,212.61
--------------
Total $486,130.33

I also don't get the answer $483,510.28