Any math geeks here? Compounding interest question

Yucca · 16 Jan 2019 at 18:09

Hi all,

I know there are a few math wiz kids on the forums so if anyone can work this out for me id appreciate it...

Im looking at the LISA's (life time ISA's) which allow you to put in 4k per year and receive a 4k bonus until the age of 50. You can then withdraw the total at 60. In addition to the bonus's lets assume there is a 1% per annum interest paid.

So from the age of 30 I put in 4k every year. Every year I get the 1k bonus. Plus I earn the 1% on the total. I do this every year for 20 years till I hit 50. Between the age of 50 and 60 (10 years) I do not add any money to the pot. I just continue to get the 1% annual interest on the total balance.

So iv put in a total of £80k, 4k per year for 20 years. What is my total lump sum at 60 adding up all the £1000 bonus's and more importantly the compounding interest of the 1% per year?!

Tried working it out. Mind totally fried!!

peterwalkley · 16 Jan 2019 at 18:34

Why not just model it on a spreadsheet. There will be a clever formula to work it out but my maths has gone too rusty to remember exactly how to do it.

touch · 16 Jan 2019 at 18:36

Roughly £109,500.

The actual amount will vary slightly, depending on a few factors:
-Do you pay your 4k into the account at the start of each year or at the end - or make equal monthly payments adding up to 4k?
-Is the bonus paid proportionally when you make deposit or added in a lump sum at the end of the year?
-Is interest paid monthly or annually?

Yucca · 16 Jan 2019 at 19:01

touch said:
Roughly £109,500.

The actual amount will vary slightly, depending on a few factors:
-Do you pay your 4k into the account at the start of each year or at the end - or make equal monthly payments adding up to 4k?
-Is the bonus paid proportionally when you make deposit or added in a lump sum at the end of the year?
-Is interest paid monthly or annually?

The guidance says:

HMRC will calculate bonus payments for your Lifetime ISA account on a month-by-month basis. Your bonus is calculated on any payments you make into your account from the 6th of the month to the 5th of the following month. Your bonus will be paid into your account within 14 days of the 20th of month two.

So I assume I can pay the 4k at the start of each year as a lump sum. But from what I understand the 25% would be split up as 12 monthly payments of approx 2% I think?! They don't make it very clear!

How did you get to the figure of £109,500?

Yucca · 16 Jan 2019 at 19:02

peterwalkley said:
Why not just model it on a spreadsheet. There will be a clever formula to work it out but my maths has gone too rusty to remember exactly how to do it.

If I knew how to do such wizardary I wouldn't have asked on here

.

platinum87 · 16 Jan 2019 at 19:18

£122,271.13

Yucca · 16 Jan 2019 at 19:21

platinum87 said:
£122,271.13

Could you please tell me how you worked that out? There is a big difference between touches figure and yours...

MM-Seat · 16 Jan 2019 at 19:26

The sum I used (which gives the same result as touch)

4000*1.01^20 = £4880.76
4000*1.01^19 = £4,832.44

And so on, till you get to;

4000*1.01^1 = £4040.00

This totals £88, 956.78 from my calculations. Then add in 20 years of £1k bonus giving me £108,956.78 (so slightly different)

I would advise speaking to a financial adviser if you aren't sure however.

platinum87 · 16 Jan 2019 at 19:28

Yucca said:
Could you please tell me how you worked that out? There is a big difference between touches figure and yours...

The easy way to work it out, is to calculate saving £5k per year for 20 years @ 1%, which will end up being £110,095.02,

Then you put £110,095.02 for 10 years no extra deposits @ 1%, and it goes to £121,613.39. That is yearly interest compounding, the first calculation was daily, or monthly i forget

platinum87 · 16 Jan 2019 at 19:28

MM-Seat said:
The sum I used (which gives the same result as touch)

4000*1.01^20 = £4880.76
4000*1.01^19 = £4,832.44

And so on, till you get to;

4000*1.01^1 = £4040.00

This totals £88, 956.78 from my calculations. Then add in 20 years of £1k bonus giving me £108,956.78 (so slightly different)

I would advise speaking to a financial adviser if you aren't sure however.

???

wtf is this man?>

MM-Seat · 16 Jan 2019 at 19:29

MM-Seat said:
The sum I used (which gives the same result as touch)

4000*1.01^20 = £4880.76
4000*1.01^19 = £4,832.44

And so on, till you get to;

4000*1.01^1 = £4040.00

This totals £88, 956.78 from my calculations. Then add in 20 years of £1k bonus giving me £108,956.78 (so slightly different)

I would advise speaking to a financial adviser if you aren't sure however.

Ignore me, I'm not taking into account the 10 years after you stop contributing

Rotty · 16 Jan 2019 at 19:29

Are you employed or self employed?

If employed you are probably better putting money into your pension than this

MM-Seat · 16 Jan 2019 at 19:30

platinum87 said:
???

wtf is this man?>

Erm... a method of working out compound interest?

touch · 16 Jan 2019 at 19:31

platinum87 said:
The easy way to work it out, is to calculate saving £5k per year for 20 years @ 1%, which will end up being £110,095.02,

Then you put £110,095.02 for 10 years no extra deposits @ 1%, and it goes to £121,613.39. That is yearly interest compounding, the first calculation was daily, or monthly i forget

This is effectively what I did but I calculated for 19 years as I assumed the first year would start from £0.

I also missed the extra 10 years of interest with no bonus.

Yucca · 16 Jan 2019 at 19:34

So........ Any idea folks lol.

MM-Seat · 16 Jan 2019 at 19:36

My calculations don't assume the £1k bonus is included in the interest calcs as both of yours do.

platinum87 · 16 Jan 2019 at 19:36

Yucca said:
So........ Any idea folks lol.

I will give you a 3rd answer, and that is £51,000 this one is more rough but its close enough.

They are all correct FYI,

MM-Seat said:
My calculations don't assume the £1k bonus is included in the interest calcs as both of yours do.

Yea interest is paid on the bonus, as the bonus is paid by the government into a normal account.

Money in that account earns interest, thus calculating it, just assume its 5k per year, not 4+1

Then you can just state 80k was his contributions and 20k was the bonus

MM-Seat · 16 Jan 2019 at 19:41

platinum87 said:
Yea interest is paid on the bonus, as the bonus is paid by the government into a normal account.

Money in that account earns interest, thus calculating it, just assume its 5k per year, not 4+1

Then you can just state 80k was his contributions and 20k was the bonus

How odd, my help to buy ISA didn't work like this.

Yucca · 16 Jan 2019 at 19:44

platinum87 said:
I will give you a 3rd answer, and that is £51,000 this one is more rough but its close enough.

They are all correct FYI,

Yea interest is paid on the bonus, as the bonus is paid by the government into a normal account.

Money in that account earns interest, thus calculating it, just assume its 5k per year, not 4+1

Then you can just state 80k was his contributions and 20k was the bonus

£51,000?! Now you have totally lost me!

Yucca · 16 Jan 2019 at 19:46

Rotty said:
Are you employed or self employed?

If employed you are probably better putting money into your pension than this

Self employed :/ My wife is employed and we ensure we maximise contributions obviously.