loan formula for deferred payments
Witek Busse
first loan payment is deferred by N number of days. I though I had it, but
I checked my numbers against a webpage,
http://www.firstfederal.com/ffcalculators.htm, and I am off by a couple of
$$ which is thrustrating me. Can anyone give me any insight on what I am
doing wrong.
Example: If the interest rate is 10%, the loan is $10,000, the deferred
period is 30 days, and the loan length is 10 years (actually the loan length
does not matter since I cannot get the correct amount total after the
deferred 30 days)
Here is what I did:
First thing is I tacked on interested to the $10K by using daily compounded
interest which in my equaiton is (principal + interest): $10082.519 by
using
V = D(1 + r/365)^365n
D is the amount deposited, r is the interest rate,
n is the number of years, and V is the final amount.
At this point I already have the wrong number, the website gets:1085.28 or I
am off by close to $3 what am I doing wrong?
thanks
WGB
Vincent Johns
> I need a formula/formulas for figuring out monthly loan payments if the
> first loan payment is deferred by N number of days. I though I had it, but
> I checked my numbers against a webpage,
> http://www.firstfederal.com/ffcalculators.htm, and I am off by a couple of
> $$ which is thrustrating me. Can anyone give me any insight on what I am
> doing wrong.
>
> Example: If the interest rate is 10%, the loan is $10,000, the deferred
> period is 30 days, and the loan length is 10 years (actually the loan length
> does not matter since I cannot get the correct amount total after the
> deferred 30 days)
>
> Here is what I did:
>
> First thing is I tacked on interested to the $10K by using daily compounded
> interest which in my equaiton is (principal + interest): $10082.519 by
> using
> V = D(1 + r/365)^365n
>
> D is the amount deposited, r is the interest rate,
> n is the number of years, and V is the final amount.
Isn't it a bit unusual to have interest on a loan compounded once a day?
I have seen banks offer continuously compounded interest on savings
accounts (amounts to very slightly more than daily compounding;
according to my calculations, continuous compounding in your example
would have given about $10,082.53 instead of $10,082.51 from daily
compounding). However, many loans that I've heard about are compounded
only monthly, corresponding to the times when payments are due.
I calculated (via a spreadsheet in MS Excel) the daily compounded
interest, rounding to the nearest $0.01 at the end of each day, and got
a total due after the 30th day of exactly $10,082.51, though I used
unbiased rounding (up to $0.005 rounded down to the nearest $0.01,
otherwise rounded up). Perhaps the other calculator uses a different
rule for rounding; changing the rule to round all fractions up to the
next higher $0.01 gave me a total of $10,082.68 after the 30th day.
> At this point I already have the wrong number, the website gets:1085.28 or I
> am off by close to $3 what am I doing wrong?
>
> thanks
>
> WGB
I did visit the Web site, but wasn't able to duplicate what you say you
found there. There is a "deferred payment" calculator, but it doesn't
allow you to defer a payment for 30 days, only 0 days (for comparison, I
assume), 60 days, or 90 days, and it displays the resulting monthly
payments. I wasn't able to get it to display $1,085.28 or $10,085.28 or
anything similar... so I suppose I was using a different calculator from
what you used.
Incidentally, any formula such as
V = D(1 + r/365)^365n ,
although it has an attractive simplicity, isn't going to account
properly for the round-to-nearest-cent calculations that take place with
every payment period (in your case, every day), so perhaps what you want
isn't necessarily a formula. But if you don't mind some small
inaccuracies, your idea is sound -- calculate the total amount due 30
days in the future, and base your formula on that amount instead of the
original value of D.
Incidentally, if you were compounding your interest monthly, my
calculations would run like this:
- Calculate interest on the principal due at the beginning of the
month (=$10,000 first time)
- Round it to the nearest $0.01
- Add it to the amount due
- Subtract the payment due to get the amount due at the beginning of
the next month (assuming the payment's on time)
Repeat these steps for each month until the amount due is close to zero
(is likely not to hit zero exactly).
-- Vincent Johns <vjo...@alumni.caltech.edu>
Please feel free to quote anything I say here.