Compound interest formula

[forskare]

What would the formula be for a savings investment of $750 initially; adding $750 every 6 months, compounded semi-annually for 10 years at 8%.

Thanks

kenn

[Stan Mathews]

Re: Compound interest formula

Google led me here.

[forskare]

Re: Compound interest formula

Hi Stan,

I found that as well but wasn't sure about it's application to my situation. After further study, I presume '1' in (1 + r) = 1 year so in my case I would need to change it to '.5'.

Thank you,

kenn

[gmeredith17]

Re: Compound interest formula

Ken,

I'm no expert but the '1' looks like a constant to me. I had a quick look at the website link and have to say they could do with putting in some better explanations. However, the FV = P (1 + r / n)Yn looks like it will do the trick. I have underlined the yn as it is a power but the editor doesn't allow superscript text.

FV = Future value
P= installment value
r= rate of return (interest rate)
n= (compound n times per year)
y= number of years

Therefore

FV= 750(1+0.08/2)[U]10*2[/U]

FV=750(1+0.04)[U]20[/U]

FV= 750*(1.04)[U]20[/U]

FV= 750*2.191123143

FV=$1643.34

Hope it helps.

Edit: The above doesn't take into account regular contributions like you asked. I will look at one of the other formulas on the link.

Geoff

[gmeredith17]

Re: Compound interest formula

There is a FV() function in alpha which might be worth looking at.

[gmeredith17]

Re: Compound interest formula

Ken,

Do you know what answer you should get? The script below should work but as I haven't ever worked with compound interest formulas I'm not sure if the end result is correct or not.

fvalue=0
p=750
y=10
r=0.08
n=2

for i=1 to y
fvalue=((fvalue+p)*(1+r/2)^n)
next i

ui_msg_box("",fvalue)

[Steve Andrews]

Re: Compound interest formula

Kenn,

If it is compounded semi-annually, you cannot simply divide the annual rate by 2 for the semi-annual rate. A rate of 4% every six months is equivalent to an annual rate of 8.16%.

A function which takes into account the compounding every six months is shown here.

FUNCTION FV_Semi_Ann(nPymt as N, nInt as N, nYrs as N)
	dim nFV as N
	dim nInt2 as N
	dim nFctr as N
	
	nInt2 = (1+nInt)^(1/2) - 1
	nFctr = ((1+nInt)^nYrs-1)/(nInt2/(1+nInt2))
	nFv = nFctr * nPymt
	
	FV_Semi_Ann = nFV
END FUNCTION

You would use this function as follows in your case:

Future_Value = FV_Semi_Ann(750,.08,10)

This function could be expanded to handle other modes (e..g. quarterly, monthly, etc.) but for now is strictly semi-annual. I hope this helps.

Steve

[gmeredith17]

Re: Compound interest formula

Steve,

Thanks for the function.

I plugged Ken's figures into an online calculator (here) which gives a different result to your function.

Do you know why this would occur?

[Steve Andrews]

Re: Compound interest formula

Geoff,

It could be one of two things. First, did the online calculator assume compounding of interest every six months? If so, the interest rate every six months would be about 3.923%. Notice that (1.03923)*(1.03923)=1.079999.

Secondly, the annuity described by Kenn is an "annuity due" since the payments are at the beginning of every period. That is what my function assumes. Also, there is an "annuity immediate" which would be where the first $750 payment would be made six months from now. To calculate for the annuity immediate, only a small tweak would have to be made to my function. Namely, I would remove the "(1+nInt2)" from the nFctr expression. But since Kenn said "$750 initially", this didn't seem to apply.

I haven't investigated the online calculator yet so I'm not sure what it may be assuming.

Steve

[Steve Andrews]

Re: Compound interest formula

Geoff,

I did take a look at the online calculator and found that it is not compounding every six months. It does assume that 4% interest is earned every six months which is 8.16% annually if compounded every six months.

Steve

[gmeredith17]

Re: Compound interest formula

Steve,

Thanks for taking the time to look and explain.

Cheers

Geoff

[G Gabriel]

Re: Compound interest formula

Not sure why do you even need a UDF?
Alpha's FV() is what you need; however there seems to be a flaw in alpha's FV() or perhaps I am missing something.

See related thread.

Interstingly enough, the amount I am getting matchs the amount given by the website calculator referenced by Geoff.

And threfore, the correct answer to Ken's original question:
A periodic investment of $750 every 6 months with annual interest of 8% paid semi annually for 10 years is:

$23,226.90



Alpha gives a different number:

?fv(750,.08/2,20)
= 22333.6

Again, and as you will see in my comments at the other thread, alpha is giveing the amount at the beggining not the end of the last period.