Compound interest question - closing account early

masonic

clairec666 said:

SacredStephan said:

clairec666 said:
Is this because the bank has adjusted the interest to negate the effect of the extra compounding? I.e. a day's interest is NOT calculated as 1/365 of the year's interest?

At the point that the interest is calculated the bank won't know about any compounding that might happen in the future. A day's interest IS usually calculated as 1/365 of the gross annual interest.

That's what I assumed, but it contradicts what Rudyson said

That comment seems to be based on the assumption of monthly interest and a lower gross rate. Banks are required to quote an AER as the most prominent rate, which has led to gross and annual interest having the same AER where both are offered as options. In theory there is nothing to stop them offering different AER rates for monthly vs annual interest options, but I suspect that would be viewed negatively.

SnowMan

clairec666 said:

SacredStephan said:

clairec666 said:
Is this because the bank has adjusted the interest to negate the effect of the extra compounding? I.e. a day's interest is NOT calculated as 1/365 of the year's interest?

At the point that the interest is calculated the bank won't know about any compounding that might happen in the future. A day's interest IS usually calculated as 1/365 of the gross annual interest.

That's what I assumed, but it contradicts what Rudyson said

I think Rudyson has just calculated it as 1,000 x 1.05 ^1/2 -1 = 1,024.69 (if you round down) and the final balance as 1,000 x (1.05 ^ 0.5) x (1.05 ^ 0.5) = 1000 x 1.05 = 1,050. And so Rudyson is probably not aware that's not how most savings providers calculate interest and so that post is missing the whole point of this discussion, that being about the usually marginally generous n/365 method used by most savings providers.

masonic

We've seen a couple of examples of institutions compounding daily, which removes this marginal gain. Though I think it would be an interesting gimmick to see an example of continuous compounding, where the balance would increase by a factor of e^(i x t) where i is the decimal rate and t is the precise length of time in units of years the money is held in the account (AER = e^i-1).

clairec666

masonic said:

We've seen a couple of examples of institutions compounding daily, which removes this marginal gain. Though I think it would be an interesting gimmick to see an example of continuous compounding, where the balance would increase by a factor of e^(i x t) where i is the decimal rate and t is the precise length of time in units of years the money is held in the account (AER = e^i-1).

If you want a real deep-dive into interest compounding, have a look at this video:
https://www.youtube.com/watch?v=IAEASE5GjdI&list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev&index=6&t=2114s&pp=iAQB
(most relevant bit starts about 3 minutes in)

masonic

clairec666 said:

masonic said:

We've seen a couple of examples of institutions compounding daily, which removes this marginal gain. Though I think it would be an interesting gimmick to see an example of continuous compounding, where the balance would increase by a factor of e^(i x t) where i is the decimal rate and t is the precise length of time in units of years the money is held in the account (AER = e^i-1).

If you want a real deep-dive into interest compounding, have a look at this video:
https://www.youtube.com/watch?v=IAEASE5GjdI&list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev&index=6&t=2114s&pp=iAQB
(most relevant bit starts about 3 minutes in)

Thanks, looks familiar, I think you shared that one with me before.

clairec666

masonic said:

clairec666 said:

masonic said:

We've seen a couple of examples of institutions compounding daily, which removes this marginal gain. Though I think it would be an interesting gimmick to see an example of continuous compounding, where the balance would increase by a factor of e^(i x t) where i is the decimal rate and t is the precise length of time in units of years the money is held in the account (AER = e^i-1).

If you want a real deep-dive into interest compounding, have a look at this video:
https://www.youtube.com/watch?v=IAEASE5GjdI&list=PLZHQObOWTQDP5CVelJJ1bNDouqrAhVPev&index=6&t=2114s&pp=iAQB
(most relevant bit starts about 3 minutes in)

Thanks, looks familiar, I think you shared that one with me before.

Quite possibly!