Principal of a loan

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Sue0113

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Feb 1, 2012
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A mortgage requires payments of $1000.00 at the end of every month for 25 years. If interest is 6% compounded semi-annually calculate the principal of the loan.
PV=PMT[1-(1+i)^-n] / i n=25x12 =300 i=6%/2 = 3% = .03
PV = 1000.00[1+.03)^-300] / .03
PV= 1000.00[1.03]^-300] /.03
PV= 1000.00[1.408745651] /.03
PV= 1000[4.695818838]
PV=4695.82
Where do I go from here?
 
Not very far!

You appear to have the wrong formula or the correct one but you've executed it incorrectly. Should be

A= P/i [1-(1+i)^-N where A = PV, i = interest (monthly), N = number or repayments

Therefore P= 1000
i= 6%/6 =1% = .01
N= 300
so A = 1000[1-(1+.01)^-300]
.01

I think you will find A= $96,946.55

Best wishes
Fedex16
 
Not very far!

You appear to have the wrong formula or the correct one but you've executed it incorrectly. Should be
A= P/i *[1-(1+i)^-N] where A = Principal, i = interest (monthly), N = number or repayments.

Therefore P= 1000 i= 6%/6 =1% = .01 N= 300

so A = 1000/.01*[1-(1+.01)^-300]


I think you will find A= $96,946.55

Best wishes
Fedex16
 
Sue0113 said:
A mortgage requires payments of $1000.00 at the end of every month for 25 years. If interest is 6% compounded semi-annually calculate the principal of the loan.
PV=PMT[1-(1+i)^-n] / i n=25x12 =300 i=6%/2 = 3% = .03
PV = 1000.00[1+.03)^-300] / .03
PV= 1000.00[1.03]^-300] /.03
PV= 1000.00[1.408745651] /.03
PV= 1000[4.695818838]
PV=4695.82
Where do I go from here?

Seems like this type of situation pops up every now and then where the loan payment period does not match the interest compounding period. Recalling some inputs by TKHunny, and others, several years ago, an equivalent monthly compounding rate derives from (1+SA/2)^2 = (1+M/12)^12
(1.03)^2 = (1+M/12)^12
1.0609 = (1+M/12)^12
1.0049386 = 1+M/12 making
M = .059263 and i = .059263/12 = .0049386

Therefore, from P = R[1 - 1/(1.0049386)^300]/.0049386, P = $156,297.22.

Constructive criticism, corrections or diversion welcomed.
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