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.
In message , Gary writes
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.
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.
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.
I thought it was pretty short this time.
Glad you think it's fair.
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?
In message , Stephen Burke writes
yes
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