Help calculating interest please!

prettyandfluffy

Can someone please tell me what the interest would be on £6,000 at 6.09% AER over 6 months? 

Thanks for any help, I don't trust my own maths!

ETA Just realised I've posted in the wrong forum, have flagged it to be moved.

JGB1955

6000x 6.09%/2 = £182.70

prettyandfluffy

JGB1955 said:

6000x 6.09%/2 = £182.70

Thank you very much.  That is in fact what I made it but my maths is so shocking I didn't believe it! 

tacpot12

Just so you are aware, JGB1955 arrived at the answer by taking the annual interest and dividing it by 2. This is not how the interest would be calculated by most commercial lenders. They would use a figure for the daily interest rate and calculated the interest over six months using the daily interest rate. Using this figure the interest is closer to £179.49.

prettyandfluffy

tacpot12 said:

Just so you are aware, JGB1955 arrived at the answer by taking the annual interest and dividing it by 2. This is not how the interest would be calculated by most commercial lenders. They would use a figure for the daily interest rate and calculated the interest over six months using the daily interest rate. Using this figure the interest is closer to £179.49.

Thank you, either way it's in the right ballpark for my purposes.  Explanation: I "borrowed" some money - towards buying a car - from joint savings to be repaid when a savings account of mine matured.  I want to repay the interest that would have been earned.

anilsinhaanni

For buying a car purpose, you can go with the car loans.

prettyandfluffy

anilsinhaanni said:

For buying a car purpose, you can go with the car loans.

I didn't want or need to get a car loan when I had savings available, I just want to put the savings account back in the position it would have been if I hadn't dipped into it.

xylophone

I didn't want or need to get a car loan when I had savings available, 

Relative also had savings available to pay in full after Px but decided to take the two year interest free finance and keep the savings earning interest.....

Exodi

I use the FV (Future Value) function on Excel, very simple to use and quick once you get comfortable with it.

=FV(Rate,Nper,PMT,PV,Type)

Rate is the interest rate per period.

Nper is the number of periods.

PMT is the monthly payment (if any).

PV is the present value (expressed as a negative).

Type is 0 if the monthly payment is made at the end of the period, 1 if made at the beginning.

Generally I just apply the formula monthly as a period but bank/products compound interest differently - the difference is usually negligible.

So the rate per period is (0.0609/12). The number of periods is 6. The monthly payment is zero as you're not making any. The present value is -6000 (I think this formula is commonly used for calculating debts, but can be used the opposite way round if you express the value as a negative). Type is irrelevant as you're not making monthly payments so we can leave this out.

This makes the complete formula:

=FV((0.0609/12),6,0,-6000) and returns the value £6,185.03. Take off your initial amount and you have £185.03 in interest.

If you cross-check this with a calculator site, you get the same result, for example: https://www.thecalculatorsite.com/finance/calculators/compoundinterestcalculator.php

Please don't take this as looking down on any other methods recommended on this thread. If I only needed a rough figure, I'd absolutely do 6000*0.0609 and just half it to get roughly 6 months of interest.

AmityNeon

Exodi said:

This makes the complete formula:

=FV((0.0609/12),6,0,-6000) and returns the value £6,185.03. Take off your initial amount and you have £185.03 in interest.

The FV function compounds over nper, so your formula compounds interest over six months but you're calculating the monthly gross interest rate by dividing the AER by 12. If we input 12 months instead of just 6, the total interest would equal £375.77, which is 6.26% AER.

The FV formula for an account paying monthly interest with an AER of 6.09% for six months would be either:

=FV((1.0609^(1/12))-1,6,0,-6000)

Or, utilising the benefit of the FV function's internals:

=FV(6.09%,0.5,0,-6000)

Both result in £180.00 interest, and both require extending to the full 12 months of compounding to equal £365.40 in interest, which is precisely 6.09% of 6000.

The simpler scenario is to assume a 6.09% gross/AER account that is closed after 6 months, resulting in theoretical interest of £182.70, which is the perfect figure in this context (if half days were possible or it was a leap year, which it will be).

The FV function is indeed especially useful to easily project estimates with monthly payments, whether it's amortisation or longer term savings/investments (even standard regular savers).

Exodi

AmityNeon said:

Exodi said:

This makes the complete formula:

=FV((0.0609/12),6,0,-6000) and returns the value £6,185.03. Take off your initial amount and you have £185.03 in interest.

The FV formula for an account paying monthly interest with an AER of 6.09% for six months would be either:

=FV((1.0609^(1/12))-1,6,0,-6000)

Or, utilising the benefit of the FV function's internals:

=FV(6.09%,0.5,0,-6000)

Both result in £180.00 interest, and both require extending to the full 12 months of compounding to equal £365.40 in interest, which is precisely 6.09% of 6000.

You're totally right re the compound period.

I'm too used to using FV for investment projections, but in the OP's case with an AER and likely a fixed product, the FV formula and period would be as you say. Thanks for pointing that out.

tacpot12 said:

Just so you are aware, JGB1955 arrived at the answer by taking the annual interest and dividing it by 2. This is not how the interest would be calculated by most commercial lenders. They would use a figure for the daily interest rate and calculated the interest over six months using the daily interest rate. Using this figure the interest is closer to £179.49.

I can't work out how you get £179.49 but based on what you said I fear you are making the same mistake I am regarding compound period.

While banks may calculate interest daily, they do not necessarily compound/pay interest daily. I may be being a bit presumptuous here, but I'd guess the OP is talking about a fixed rate bond. Calculating interest daily is mostly intended for easy access accounts with fluctuating balances, or for debts. It's fairly meaningless in the context of fixed savings accounts. Plus this is why AER's are used in the first place.

In that case you would expect the interest paid over 6 months to be exactly half that of the AER over a year.

The bank calculating the interest daily is a red herring, their back end systems would merely look like this:

Day 0: +£6,000
Day 1: +£1.001... (£6,000 x 6.09%/365=0.016685...%)
Day 2: +£1.001... (£6,000 x 6.09%/365=0.016685...%)
Day 3: +£1.001... (£6,000 x 6.09%/365=0.016685...%)
...
Day 365: +£1.001... (£6000 x 6.09%/365=0.016685...%)
----
Total: £6,365.40 (£6,000*(1+0.0609))