For a bank loan I owe, I need to make 10 more monthly paymnets $1000
each(at the end of each month). The interest rate is 12% per year. My
finances require that I stretch these payments out so that I can repay
the remaining balance by paying only $700 per month. How many months
will it take now to pay off my loan?

Holla –

This problem requires one to calculate the present value of the 10
monthly payments at $1,000  each in order to start.  Basically at the
end of month 10 you'll be paying $990.10 in principal and
$9.90 in interest.

For month 9, you'll be paying interest on the remaining principal for
months 10 and 9 – but we don't know month 9's principal.  However
subtracting the INTEREST portion for month 10, gets you there:
$1000 = Mo(10) interest + Principal(9)*0.01 + Principal(9)
$990.10 = Principal(9)*.01 + Principal(9)

algebraically, this is  $990.10=1.01x; x = $900.10 

The easiest way to take present values backwards is in Excel, as in
the previous answer on the annuity.  To find a PV in Excel of what
remains on your 10 payments:
PV(rate,nper,pmt,fv,type)

rate = interest rate expressed in decimals
nper = number of payment periods in the annuity
pmt = payment made each period
fv = balance after last payment (0 in this case)
type = whether payments are beginning or end of period 

Your current principal owing is $9,471.30.

Now, how long will it take to pay that down a $700 per month?

You can also go through month-by-month this way:
MO 0: principal = $9,471.30
MO 1: interest = $94.71
           balance paid = $700 - $94.71 = $605.29
           principal = $8,866.01

etc.

Excel's number of periods function returns the payment information for
a set number of payments on a loan at a fixed rate.
NPER(rate, pmt, pv, fv, type)

rate = interest rate expressed in decimals
pmt = payment made each period
pv = present value or current loan = $9,471.30
fv = balance after last payment (0 in this case)
type = whether payments are beginning or end of period 

This takes the loan period from 10 months to 14.6 months.
Best regards,

Omnivorous-GA

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Clarification of Answer by omnivorous-ga on 10 Dec 2002 17:08 PST

Holla --

I think that you've misinterpreted the sentence with the answer.  The
answer is: it will NOW take you 14.6 months.

The sentence merely says that you go from the old term of 10 months to
a NEW term of 14.6 months.  It is not a range.

Best regards,

Omnivorous-GA

the question was not clearly answered. There should be a certain
percent and not a range.