1. Home
  2. UK Finance Discussions
  3. Compound intereset calculators - different results.
  4. Page 5

Compound intereset calculators - different results.

"Andy Pandy" wrote

If that is what it is meant to be, then it is not necessarily the **force of interest**.

"Andy Pandy" wrote

How do you go between your FoI#2(t) function and the corresponding "balance"/"value" function V(t)?

There are clearly defined formulae to get V(t) from FoI(t), and similarly to get FoI(t) from V(t), when FoI is the *true* force of interest.

"Andy Pandy" wrote

I must have missed something - *what* exactly does it "say on the tin"??

"Andy Pandy" wrote

I only noticed you define it as: (1) formula is z(t) = r/(1+r(1-t)); then later by: (2) z(t-dt) = z(t) - z(t)^2dt

If something is just defined by a formula (as here) then of course it is "correct as defined"!

The true force of interest, on the other hand, is defined by its relationship with the value function. The two go together. Given one, you can determine the other.

For instance, if you consider your FoI#2 function to be a *true* force of interest, then its value function is (as shown earlier) :- V(t) = V(0) / [ 1 - i.t/(1+i) ]

This means that the accrued interest, (i.t), is being discounted (for (1-t) years) at a rate of :- (1 + i - i.t)^(1/(1-t)) - 1

At t=0, this is equal to i -- eg 6% [if AER=6%]. At t=0.5, this is equal to (1+i/2)^2-1 - eg 6.09% [if AER=6%]. As t tends towards 1, this is around 6.18% [if AER=6%].

Reply to
Tim
Loading thread data ...

"john boyle" wrote

Hold on - you said the nominal rate was 9.819% (see snippet of your comments above).

You were arguing *against* using nominal 10% (as we were doing) !!

Reply to
Tim

In message , Tim writes

At that point in the thread I was arguing against Andy Pandy's assertion as to which account was the *best* place to put your money for a fixed period and was using the AER as it would be quoted in an advert for a three month fixed period deposit. In the scenario you are suggesting then this is an ongoing investment and in those circs if the account pays interest annually then the AER regs allow you to assume that the interest is paid annually and that the period used for the purposes of an AER calc ends on the day the interest is credited to the account.

Reply to
john boyle

Actually, HBoS websaver pays on the anniversary of opening. Granted that may not be typical.

Reply to
Ronald Raygun

"john boyle" wrote

I'm now thinking about the type of account where you need to make a regular monthly deposit of (say) upto 250pm, for a period of exactly 12 months, and you get an enormous (nominal) rate of, say, 7%pa. [Suppose interest is paid annually, applied (& then compounded), in exactly

12 month's time at 7.00%.]

A single deposit at the start of the year would earn 7% interest, so AER would be 7.00% (for a single deposit). But with 12 separate deposits at monthly intervals, the AER would be (let's hope I'm right here!) ... 7.07%.

How does this example tie-in with your comments above? Should the bank quote AER=7.00% (the effective rate a 'single depositer' would obtain) or AER=7.07% (the effective rate a 'regular saver' would obtain) ??

From Halifax's offering at 6% quoting AER=6.05%, I'd guess the latter. But this *does* "... vary with the transaction pattern ..." (as shown above) - contrary to your comments....

Reply to
Tim

In message , Tim writes

I said to AP 'in the way you describe'.

The AER rules differentiate between those accounts in which the regular contribution is contractual (which is the case of the account to which you refer) and those in which the transactions are discretionary. In the case of the former then the calculation is as you describe, in the latter then the transactoins make no difference. E.g. the Halifax basic savinmgs accounts have AERs which are the same as the Gross Interest rate.

Reply to
john boyle

"john boyle" wrote

Does that mean that two contracts could quote "7.07% AER" (the 'former' type above) and "7.00% AER" (the 'latter' type above), and a person who was going to save regularly anyway (so that the contractual restriction to save regularly has no effect on him) would get the *same* interest from both (7% nominal)? Even though the former account "looks" better, with a higher AER? Isn't that a failing of the AER rules??

Reply to
Tim

In message , Tim writes

Yes.

Reply to
john boyle

BeanSmart website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.