View Full Version : Loans and APR's

Gary

August 7th 03, 12:59 AM

Hi

How do you work out loan repayments with the quoted APR's?

e.g. £2000 over 2 years @ 7.3% APR

How would you work out the repayments?

I know it not as simple as adding 7.3% to the loan amount of £2000 then

dividing by 24.

Always wondered, but never asked.

--

Gary

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john boyle

August 7th 03, 01:33 AM

In message >, Gary

> writes

>Hi

>

>How do you work out loan repayments with the quoted APR's?

>e.g. £2000 over 2 years @ 7.3% APR

Within a very short time indeed a chap with the initials 'RR' will reply

with a very accurate, but long, explanation of the mathematical APR

calculation.

Unfortunately, his model starts form the other end, i.e. with a known

pattern of repayments. You are asking what the payments will be from a

stated APR. RR will make some assumptions for his calculation, which is

fair enough.

My Answer is that you cant back calculate the repayments from a given

APR without knowing the lenders adopted interest calculation method and

any other charges that may be applied. (There may be a £100 arrangement

fee paid on day 7, for example), or it might be ,001% interest per annum

with a £1000 fee. Without this info it cant be done.

--

john boyle

Ronald Raygun

August 7th 03, 10:30 AM

Gary wrote:

> Hi

>

> How do you work out loan repayments with the quoted APR's?

> e.g. £2000 over 2 years @ 7.3% APR

Generally you can't, because as a rule APR is a legal constrcution

derived from the nominal rate which the lender really applies, and

usually quotes too.

> How would you work out the repayments?

Making the usual assumptions, i.e. that there are no extraneous

fees etc, and that in fact there is a fixed monthly rate with

monthly compounding, and that the 7.3% figure is not the result

of too much rounding, you can recalculate the monthly rate by

taking 1 from the 12th root of 1.073, giving 0.5889% per month,

or a nominal 7.067% per year.

Then the repayments are £2000*0.005889/(1-1.005889^-24) = £89.61.

Ronald Raygun

August 7th 03, 10:45 AM

john boyle wrote:

> Within a very short time indeed a chap with the initials 'RR' will reply

> with a very accurate, but long, explanation of the mathematical APR

> calculation.

I thought it was pretty short this time.

> Unfortunately, his model starts form the other end, i.e. with a known

> pattern of repayments. You are asking what the payments will be from a

> stated APR. RR will make some assumptions for his calculation, which is

> fair enough.

Glad you think it's fair.

> My Answer is that you cant back calculate the repayments from a given

> APR without knowing the lenders adopted interest calculation method and

> any other charges that may be applied.

Too true. But you can always assume there are no other charges.

As a matter of interest (groan), do you know of any lenders who

apply interest on a true continuous exponential basis instead of

linearly? Typically a deal with monthly repayments might involve

payment being taken and calculated on the same day relative to the

start or end of a month, possibly deferred to the next working day

if the day falls on a weekend or holiday, and so the actual periods

will be of varying length.

So I guess most will tend to do a calculation on the payment date

such that they will charge interest on the previous balance at

(number of days since last payment) / (days in year) times

(nominal annual interest rate), and will add this amount to the

balance while deducting the actual monthly payment, to arrive

at the new balance, and hope it all works out in the end, with an

adjustment if necessary to the very last payment.

Does anyone instead charge interest on the basis ((APR+1) to the

power ((number of days since last payment) / (days in year)))-1?

john boyle

August 10th 03, 12:09 AM

In message >,

Stephen Burke > writes

> are lenders allowed to

>charge an extra day's interest?

>

yes

--

john boyle

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