Help to add to a compound interest formula

[ss]

I dont understand the formula as I googled it, it is for a multiple
compound interest on £16,000 pounds the interest rate being 8.7%

=FV(8.7%/12,24,,-16000).

I can play with the figures to adjust the %, the amount and the time scale.
How would I (if possible) add to this formula to deduct 18% off the
interest in order to give me a Net total, its currently a gross figure.
I can adjust the 8.7% (gross) figure downward to get near enough but
would prefer to be more accurate if only for tidyness.

thanks

 

[joeu2004]

I dont understand the formula as I googled it,
it is for a multiple compound interest on £16,000
pounds the interest rate being 8.7% =FV(8.7%/12,24,,-16000).
I can play with the figures to adjust the %,
the amount and the time scale. How would I
(if possible) add to this formula to deduct 18%
off the interest in order to give me a Net total,
its currently a gross figure. I can adjust the 8.7%
(gross) figure downward to get near enough but would prefer to be more
accurate if only for tidyness.

I am very familiar with these types of formulas, but I do not understand
what you mean by "deduct 18% off the interest in order to give me a net
total".

Can you give us a concrete example? Use your "near enough" estimate to show
us what the final result should be.

Literally, this is what "18% off the interest" might mean to me. I will
explain it in steps so that you might understand better and/or tweak my
misunderstanding, if any.

FV(8.7%/12,24,,-16000) is the total future value of investing 16000 over 24
months at 8.7%/12 per month.

(By the way, 8.7%/12 might not be the right monthly rate for your purposes.
We can discuss that later.)

So FV(8.7%/12,24,,-16000)-16000 is the total interest. Ergo:

(FV(8.7%/12,24,,-16000)-16000)*(1-18%)

is "18% off the interest", based on one interpretation.

So the total future value with "18% off the interest" would be:

=16000+(FV(8.7%/12,24,,-16000)-16000)*(1-18%)

That is algebraically equivalent to:

=16000*18%+FV(8.7%/12,24,,-16000)*(1-18%)

 

[ss]

I am very familiar with these types of formulas, but I do not understand
what you mean by "deduct 18% off the interest in order to give me a net
total".

Can you give us a concrete example? Use your "near enough" estimate to
show us what the final result should be.

Literally, this is what "18% off the interest" might mean to me. I will
explain it in steps so that you might understand better and/or tweak my
misunderstanding, if any.

FV(8.7%/12,24,,-16000) is the total future value of investing 16000 over
24 months at 8.7%/12 per month.

(By the way, 8.7%/12 might not be the right monthly rate for your
purposes. We can discuss that later.)

So FV(8.7%/12,24,,-16000)-16000 is the total interest. Ergo:

(FV(8.7%/12,24,,-16000)-16000)*(1-18%)

is "18% off the interest", based on one interpretation.

So the total future value with "18% off the interest" would be:

=16000+(FV(8.7%/12,24,,-16000)-16000)*(1-18%)

That is algebraically equivalent to:

=16000*18%+FV(8.7%/12,24,,-16000)*(1-18%)

I will work through your explanation and see if I can work it out.

using my formula and trying to be clearer...
8.7% =FV(8.7%/12,24,,-16000)

8.7% is the interest the bank gives me on £16000 (but it is Gross)
over 2 years the total with interest is now £19029 (£16000 compounded at
8.7% over 24 months)

So the interest the bank has given me is £3029 (but that is a gross
figure so I need to deduct tax off the interest only at 18% so the
figure I require to achieve would be approx £2483 + £16000 = £18483
So...£16000 + 8.7% compound, minus 18% for tax.

The account is a time deposit account and the interest is added every 30
days with tax deducted at source, so what I am trying to do is forecast
what I can earn over a period of months as a Net figure.

 

[joeu2004]

8.7% is the interest the bank gives me on £16000
(but it is Gross) over 2 years the total with interest
is now £19029 (£16000 compounded at 8.7% over 24 months)

So the interest the bank has given me is £3029
(but that is a gross figure so I need to deduct tax off
the interest only at 18% so the figure I require to
achieve would be approx £2483 + £16000 = £18483
So...£16000 + 8.7% compound, minus 18% for tax.

The account is a time deposit account and the interest
is added every 30 days with tax deducted at source

Much better description!

The effective after-tax annual rate is 8.7%*(1-18%). So ostensibly:

=FV(8.7%*(1-18%)/12,24,,-16000)

which results in about $18446.

-----

However, I am a bit surprise that if a UK bank specifies an annual rate of
8.7%, the monthly rate is about 8.7%/12.

It is my understanding that UK banks specify a compounded annual rate. In
that case, the monthly rate would be (1+8.7%)^(1/12)-1. And the effective
after-tax monthly rate would be ((1+8.7%)^(1/12)-1)*(1-18%). So your
formula would become:

=FV(((1+8.7%)^(1/12)-1)*(1-18%),24,,-16000)

which results in about $18347.

But I consider you to be the "expert" on this point, since I have never
dealt with UK banks directly.

-----

One last point.... You mention that interest is added "every 30 days", not
"every month". There is a difference.

It is possible that the bank uses either a compounded 30-day rate or a
simple 30-day rate based on the compounded annual rate of 8.7%.

The compounded 30-day rate would be (1+8.7%)^(30/365)-1. The simply 30-day
rate would be 30*((1+8.7%)^(1/365)-1). Multiply each times 1-18% to derive
the effective after-tax rate.

Or the bank might use a simple 30-day rate based on the simple annual rate
of 8.7%, to wit: 8.7%*30/365.

In all such cases, the number of periods (24) is the total days of the time
deposit divided by 30. If that is not an integer multiple of 30 days, that
complicates the FV formula.

On the other hand, perhaps you do not require so much detail, and the
original assumptions are "close enough".

 

[ss]

Much better description!

The effective after-tax annual rate is 8.7%*(1-18%). So ostensibly:

=FV(8.7%*(1-18%)/12,24,,-16000)

which results in about $18446.

-----

However, I am a bit surprise that if a UK bank specifies an annual rate
of 8.7%, the monthly rate is about 8.7%/12.

It is my understanding that UK banks specify a compounded annual rate.
In that case, the monthly rate would be (1+8.7%)^(1/12)-1. And the
effective after-tax monthly rate would be ((1+8.7%)^(1/12)-1)*(1-18%).
So your formula would become:

=FV(((1+8.7%)^(1/12)-1)*(1-18%),24,,-16000)

which results in about $18347.

But I consider you to be the "expert" on this point, since I have never
dealt with UK banks directly.

-----

One last point.... You mention that interest is added "every 30 days",
not "every month". There is a difference.

It is possible that the bank uses either a compounded 30-day rate or a
simple 30-day rate based on the compounded annual rate of 8.7%.

The compounded 30-day rate would be (1+8.7%)^(30/365)-1. The simply
30-day rate would be 30*((1+8.7%)^(1/365)-1). Multiply each times 1-18%
to derive the effective after-tax rate.

Or the bank might use a simple 30-day rate based on the simple annual
rate of 8.7%, to wit: 8.7%*30/365.

In all such cases, the number of periods (24) is the total days of the
time deposit divided by 30. If that is not an integer multiple of 30
days, that complicates the FV formula.

On the other hand, perhaps you do not require so much detail, and the
original assumptions are "close enough".

Thanks you for your help. The accuracy above should be sufficient.

Although I have quoted in £s as thats easier for me, the bank is in
Turkey and they do various time deposits 17 day, 30 day, 32 day.
Unfortunately for me 3 years ago they were still giving 18% interest,
late as always :-( I just hope the exchange rate now plummets as that
could be a good return (if it drops far enough) converting back to sterling.
In any case the interest in UK banks is only .025% so I reckon I am in a
win/win situation with Turkey either better interest rates or converting
back.

Thanks again for your help