$Contract Crediting Rate Formula$

Question

$Contract Crediting Rate Formula$

Hi,
I'm stuck on backing into the gross crediting rate (1.93%). I have all the variables and the formula but I can't come up with the answer that is provided. I'm trying to find the gross crediting rate of a contract with the formula
Gross crediting rate = (MV/CV)^(1/D)*(1+AYTM)-1;
MV = market value
CV = contract value
D = duration
AYTM = annualized yield to maturity = (1+ YTM/2)^2-1
Inputs

Market Value	48,000,000.00
Contract Value	50,000,000.00
MV/CV	96.0%
Duration	3.0 years
Yield to Maturity	3.30%
Annualized Yield to Maturity	3.33%
Gross Crediting Rate	1.93%

If I step through the formula
(MV/CV) = .96
(1/D)=.33 (.96)^.33 =.9866
(1+AYTM) = (1+.333) = 1.333
(.9866)* 1.333=1.31
1.31 - 1= .31
I'm not getting something right where I'm coming up .31 and the solution has 1.93; any suggestions?
The other part I'm stuck on is how AYTM=3.33 when (1+.33\)^2-1=.7689

I appreciate the input!

Math Finance

Pasta157

7

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You are making a mistake with percentages.

Note that $YTM=3.3 \%=0.033$. So you should substitute $YTM$ by $0.033$ and not $0.33$. If you do this you will get

\[AYTM = (1+ YTM/2)^2-1=(1+0.033/2)^2-1=0.03327=3.327\% \approx 3.33 \%.\]

You are making the same mistake when you say
\[1+AYTM = (1+.333) = 1.333.\]
Indeed we have
\[1+AYTM = (1+.0333) = 1.0333.\]
Then
\[(MV/CV)^{1/D}*(1+AYTM)-1=(0.96)^{1/3}*(1+0.0333)-1=0.01933477456\approx 0.0193=1.93 \%.\]

Daniel90

436

Pasta157

0

Thank-you! I made a rookie oversight. Greatly appreciate the help

$Contract Crediting Rate Formula$

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