finding amount of interest

[Sue0113]

You start to save for a major purchase. You can invest $500 every 3 months for 10years.
You are able to earn 8% compounded semi-annually. What is the amount of interest that you
earn during the entire term?
I believe the formula is Future Value of a simply annuity due.
FVn(due)=PMT[(1+i)^n-1/i](1+i)

500[(1.040^40-1/.040/(1.04) pmt=500 i=.04 n=10(4)
(95.02551570)(1.04)
(47512.75785)(1.04)
49413.27
40X500=20,000 so 49413.27-20,000=29413.27
Could someone please tell me where I made mistake........thanks

 

[rbcc]

Hi, what i think is

You start to save for a major purchase. You can invest $500 every 3 months for 10years. You are able to earn 8% compounded semi-annually. What is the amount of interest that you earn during the entire term?

it says "every 3 months" that corresponds to you making payments quarterly. But the interest is given to you compounded semi annually, so...

k= [(1+(0.08/2))^(2/4)]-1=0.1980

Now lets calculate the future value with that interest rate

FV= (((1+0.1980)^(10*4) -1)/0.1980)*500
=30072.94

without the interest you would have gotten

500(4*10)=20 000

now subtract those 2 values and you have it

30 072.94-20 000=10 072.94

* I don't know if it is an annuity due, the question does not say that the payments are being made at the beginning of the period

 

[Sue0113]

Thanks

I got confused because we are doing annuities so worked as annuity due.
my interest rate was wrong.
I'm not understanding how you got the interest rate you did.
I thought was .08/2 as is semi annually but didn't realize I had to but to power of 2/4
Thanks for the help!

 

[rbcc]

it could be an ordinary annuity

also the interest rate that you are given is compounded semi annually but you are making the payments quarterly ( every 3 months) you can use this formula k= [(1+(r/n))^(n/m)]-1 to "convert" the interest rate so it matches up or a formula like that which you have in your book.