"via135" wrote:
can i have a formula to find out the EMI for the
loan together with the intt as well as the FV of my loan?

Good explanation, this time. But either I do not understand
something, or something else is amiss.

First, I assume that "10% pa" means 10% per annum. But
is that the nominal rate (i.e, 10%/12 monthly), or is it the
effective annual rate -- that is, the monthly rate is
RATE(12,,-1,1+10%) = (1+10%)^(1/12) - 1?

I assume it is the nominal rate. But the bigger question is ....

You said that the 10000 rupee principal is paid off in 15
months, and the simple interest on the declining balance is
accumulated into another account, which is subsequently paid
off in 3 additional months (interest-free!). You are looking for
equal monthly payments that pays off both. Right?

Based on that description, I model the accumulated interest
as follows (i is the period interest rate, 10%/12 in your case,
and "pmt" is the monthly payment, what you call EMI):

Period 1: 10000 * i
Period 2: (10000 - pmt) * i
Period 3: (10000 - 2*pmt) * i
.....
Period 15: (10000 - 14*pmt) * i

Is that what you intended?

If so, the formula for the accumulated interest is (n is the
number of periods, 15 in your case):

int = pmt * i * n * (n+1) / 2

In order to pay off the 10000 principal alone in 15 months,
the periodic payment __must__ be 666.67 = 10000 / 15.

But there is no a priori guarantee that that periodic payment
would pay off the accumulated interest in 3 months -- unless
the interest rate had been determined based on that requirement.

In fact, with the terms of the loan you stated -- principal of
10000, 10% nominal annual rate, 15 payments -- the
accumulated interest is mathematically equal to __one__
payment, 666.67, not taking rounding into account. So the
accumulated interest could be paid off in __one__ additional
equal payment, not 3. Did you misstate the terms of the loan?

That makes more sense to me, from a business perspective.
It does not make sense that a lender would permit you to
accumulate interest and pay it off over time without charging
interest on the remaining balance of unpaid interest. It __does__
make some sense that a lender might structure a loan such
that you pay off the principal first, then you pay off the
accumulated interest in one more equal payment. The lender
loses the cost of capital (interest) on the accumulated interest
for one period. But it is simple for both the lender and borrower
to understand.

Thus, from the lender's perspective, the problem becomes:
determine the number of periods, n, or the periodic interest
rate, i, to pay off a loan in n periods plus the accumulated
interest in k more periods. Interestingly, the loan amount does
not matter.

i = 2 * k / n / (n+1)

n = SQRT((1 + 8*k) / 4 / i) - 0.5

Note: There might a simpler way to approximate n that
eludes me at the moment.

The periodic payment (pmt, emi) is simply the loan amount
divided by the number of periods, n.

pmt = prin / n ("prin" is the loan amount)

int = pmt * i * n * (n+1) / 2 ("int" is accumulated interest)

Of course, all of this is predicated on my understanding of
the method for computing accumulated interested above.
If that is wrong, all of the above is probably wrong. GIGO.

Please let me know if I have any misunderstandings. If not,
let me know if you need further explanation or translation
into Excel formulas. And please confirm any misstatement
of the terms of the loan.


-----

"via135" wrote:
i need a formula to get the result for the following:

i am getting a loan of Rs10000/- @ 10% pa with monthly rests and the
loan is payable in 18 months (15 months for principal and 3 months for
interest portion). can i have a formula to find out the EMI for the
loan together with the intt as well as the FV of my loan? hlp pl..??!!

i give below the meanings for my terminology!

1) "/" nothing but decimal separator "." and "-" means "no decimal"

2) "monthly rests" means interest being applied for monthly products
ie, month end balance.
3) interest is applied on "simple interest basis" and not on
"compounding effect". ie, interest is applied for the month end balance
of principal amount and the interest amount is transferred to another
account for which no interest is applied. that's why the repayment is
being separately fixed for principal & interest.

4) EMI means Equated Monthly Instalments..?

-via135