Compound intereset calculators - different results.

What do you mean by "flat rate"? Do you mean the mortgage rate rather than the APR?

The above sounds right if you repay the loan monthly, and your lender gives you immediate interest benefit for every overpayment (I think most do now, but some may still operate on an "annual rest" basis which means overpayments don't reduce the interest you pay till the end of the year).

No, the above assumes the whole lump sum is repaid at the end of the 5 years. If you borrowed 8000 at 5.19% and made no repayments/overpayments at all, the

In message , listerofsmeg writes

Mr R Raygun will be along in a minute. Whilst we wait whilst he oils his slide rule and cleans his new varifocals, I would point out that IF the rate is 5.19% FLAT then the payment would be £167.93, and compound interest doesnt come into it. FLAT means ((5.19 x the number of years x the amount borrowed /100) + the amount borrowed)/ the number of months.

Just compare the mortgage APR with the alternative loan APR.

Well, £151.67 is the payment which corresponds to an *actual* (as opposed to *flat*) rate of 5.19% per year: 5.19%pa = 0.4325%pm, P = Ar/(1-(1+r)^-n) = £8k*0.004325/(1-1.004325^-60) = £151.67.

But 5.19% flat for 5 years means 25.95% in all, and so the total repayable including principal is 125.95%. Over 60 months that's a bit under 2.1% per month, or £167.93 for £8000.

What do you mean *un*fortunately? Flat rate advertising shouldn't be allowed any longer. In fact, it isn't. Is it? Well, it certainly isn't allowed *not* to advertise APR.

Well, that just goes to show what to expect when using other people's calculators, especially web-based ones, especially if you just type in numbers without understanding what they bloody well mean. There's no substitute for doing the arithmetic oneself. It's terrible that people don't find out why they went to school until many years after they leave.

You scurrilous rogue, you. I'll have you know that I'm nowhere near old enough to succumb to the marketing blurb extolling the virtues of varifocals. I'm still not fully convinced that going for bifocals was a good idea, and there are times when I feel more comfortable with my old unifocals. Varifocals? No Way! Not Never, Not No-How!

Oops, yes, that's what I meant. I obviously have my terminology wrong. Have pity on the newbie!

Aha! I see now. Many thanks for clearing that up.

ps. I hate working with APR 'cus I don't understand what it is! As far as I am aware it takes into account other costs such as "arrangement fees" etc to allow a direct like for like comparison. This is great for comparisons, but not so great for working out actual repayment figures. Unless I've got it wrong that is! (More than likely)

Pretty much, but it also takes into account the frequency of interest payments. The APR equals the rate if there are no fees and interest is paid once a year at the end of the year.

With a mortgage of course the interest is paid monthly, so a 5.19% mortgage rate is really a 0.4325% monthly rate, which when compounded gives an annual rate of about 5.32%...this is the APR if there are no fees.

Except the mortgage APR will probably be next to useless, as it'll include all sorts of fees which may not be relevant to the extra borrowing, and if he's on a discounted rate it'll reflect the rate over the whole term rather than just the current rate.

In message , Andy Pandy writes

Not quite. It is that rate of discount which, if applied to a discounted cash flow comprising all of the payments made under the loan agreement, gives a net present value equivalent to the amount borrowed.

Its the *if interest paid once a year* bit that is wrong. That is the definition of AER.

Only with some loans.

I'm sure you're right, but doesn't it work out to the same thing when there are no fees?

If I took out a loan where interest was charged once a year at the end of the year and there were no fees, wouldn't the APR always be equal to the interest rate charged?

But isn't AER equal to APR if (as I specified) there are no fees?

... "Andy Pandy" wrote

Hmmmm. Using the method in the first quote above, the monthly rate would be

Which do you prefer? ;-)

Yes, quote 1 was the result of some online compound interest calculator so it must have assumed 5.19% APR (or should that be AER), rather than a mortgage type loan where the quoted annual rate is really the monthly rate times 12.

No, because APR takes into accountwhen the actual payments are made, not when interest is charged. For example, many loan repayments are calculated on the basis that interest is charged once a year, and borrower payments are applied to the loan account once a year, but nevertheless payments are

But if you could find a loan deal where you *really* only have to make annual payments, and not monthly ones, then yes, I think you'd be right. The nominal rate would equal the APR.

The term AER is only used for saving, and APR is used only for borrowing, so to compare them is meaningless.

"Ronald Raygun" wrote

Surely not "meaningless"?

If you found a loan with an APR of 5.8% (say), and a savings a/c with an AER of over 6% - is it not worthwhile comparing the two, to deduce that you could make a little money there? [Assume non-taxpayer, or that the savings a/c is tax-free.]

In message , Andy Pandy writes

No the method of application of interest also matters

Likekly, it would be so, so long as the interest was applied on the last day of the accrual period and any changes of balance were refelcted in the daily interest that accrues.

No, see above, but I take your point.